# What am I missing??

#### GroJo

##### New member
I started doing complex fraction solving, and for some reason, i cant get this simply one solved. I know the answer, but still have no idea how to get it....

Problem: (4/5 + 2/3)/((5/8 -1/4) Answer: 11 11/15

Solving method by me: (4/5 + 2/3) = 22/15
(5/8 - 1/4) = 3/8? this is where i get lost. I know the top one to be correct.... but my bottom fraction of the equation doesnt add up to the answer.

(22/15)/(3/8) = 22*8= 176 15*3=45 176/45 or 3 & 41/45.

I know that 176 is correct because 11 & 11/15 = 176/15

Where I get lost is why do I keep coming up with 45 for my denominator in my final answer.

For the top part of my answer i concluded 15 To be my LCD and concluded (4/5*3/3) + (2/3*5/5) to get 22/15
For the bottom i thought 8 would be my LCD and concluded (5/8 *1/1) - (1/4 * 2/2) to get 3/8

It seems to me in order to get the right answer my numerator in the bottom part of the equation (the 3/8) should actually equal 1/8, so when i flip it to get my reciprocal, my equation to get my final answer should be 22/15*8/1 but i get 22/15*8/3. Where am i going wrong??

#### Subhotosh Khan

##### Super Moderator
Staff member
I started doing complex fraction solving, and for some reason, i cant get this simply one solved. I know the answer, but still have no idea how to get it....

Problem: (4/5 + 2/3)/((5/8 -1/4) Answer: 11 11/15

Solving method by me: (4/5 + 2/3) = 22/15
(5/8 - 1/4) = 3/8? this is where i get lost. I know the top one to be correct.... but my bottom fraction of the equation doesnt add up to the answer.

(22/15)/(3/8) = 22*8= 176 15*3=45 176/45 or 3 & 41/45.

I know that 176 is correct because 11 & 11/15 = 176/15

Where I get lost is why do I keep coming up with 45 for my denominator in my final answer.

For the top part of my answer i concluded 15 To be my LCD and concluded (4/5*3/3) + (2/3*5/5) to get 22/15
For the bottom i thought 8 would be my LCD and concluded (5/8 *1/1) - (1/4 * 2/2) to get 3/8

It seems to me in order to get the right answer my numerator in the bottom part of the equation (the 3/8) should actually equal 1/8, so when i flip it to get my reciprocal, my equation to get my final answer should be 22/15*8/1 but i get 22/15*8/3. Where am i going wrong??
$$\displaystyle \displaystyle \frac{\frac{4}{5} + \frac{2}{3}}{\frac{5}{8} - \frac{1}{4}}$$

$$\displaystyle = \ \displaystyle \dfrac{\dfrac{22}{15}}{\dfrac{3}{8}}$$

$$\displaystyle = \ \displaystyle \frac{22}{15} * \frac{8}{3}$$

$$\displaystyle = \ \displaystyle \frac{22 * 8}{15 * 3}$$

You did not go wrong any where - if the posted problem is correct.

One way the given answer would be correct - if the problem was to simplify: (4/5 + 2/3)/((5/8 -1/2)

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#### srmichael

##### Full Member
I started doing complex fraction solving, and for some reason, i cant get this simply one solved. I know the answer, but still have no idea how to get it....

Problem: (4/5 + 2/3)/((5/8 -1/4) Answer: 11 11/15

Solving method by me: (4/5 + 2/3) = 22/15
(5/8 - 1/4) = 3/8? this is where i get lost. I know the top one to be correct.... but my bottom fraction of the equation doesnt add up to the answer.

(22/15)/(3/8) = 22*8= 176 15*3=45 176/45 or 3 & 41/45.

I know that 176 is correct because 11 & 11/15 = 176/15

Where I get lost is why do I keep coming up with 45 for my denominator in my final answer.

For the top part of my answer i concluded 15 To be my LCD and concluded (4/5*3/3) + (2/3*5/5) to get 22/15
For the bottom i thought 8 would be my LCD and concluded (5/8 *1/1) - (1/4 * 2/2) to get 3/8

It seems to me in order to get the right answer my numerator in the bottom part of the equation (the 3/8) should actually equal 1/8, so when i flip it to get my reciprocal, my equation to get my final answer should be 22/15*8/1 but i get 22/15*8/3. Where am i going wrong??
You are correct. It should be 176/45. Where did 176/15 come from? Is that the book's answer or the teacher's? Either way, they are wrong.

#### GroJo

##### New member
this was a problem on an online coarse im taking, and if everyone agrees im correct in my solving, then i question the credibility of this site.

i thought the same thing that to get the answer they say is correct the equation would end up needing to be (4/5 + 2/3)/(5/8 -1/2)

and yes that is the equation, ill copy and paste for sh*ts and giggles :
(4/5 + 2/3)/(5/8 - 1/4)

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#### srmichael

##### Full Member
this was a problem on an online coarse im taking, and if everyone agrees im correct in my solving, then i question the credibility of this site.
I have found many errors in these online coarses when i tutor kids taking these classes. It is really frustrating for them, like you are experiencing now, where they do the problem correctly and it does not match the computer's answer. So natually they think they did something wrong when, in fact, it's the computer's error.

#### GroJo

##### New member
Is there any site you would recommend. Im brushing up on my algebra, since its been years since i have done them. Im perusing a degree in physics, and for obvious reasons, i need creditable information to do so. I know a class room setting would be best, but I am disabled and have a son at home that I have to take care of. Any help would be , well helpful

And since i cant spell pursuing correctly, I could use some spelling courses to lol

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#### GroJo

##### New member
Gros Joseph? Tu est un frog comme moi?
Qu'entendez-vous im comme une grenouille?

#### JeffM

##### Elite Member
Is there any site you would recommend. Im brushing up on my algebra, since its been years since i have done them. Im perusing a degree in physics, and for obvious reasons, i need creditable information to do so. I know a class room setting would be best, but I am disabled and have a son at home that I have to take care of. Any help would be , well helpful

And since i cant spell pursuing correctly, I could use some spelling courses to lol
I am tutoring a kid in algebra at the local library. I found several algebra review texts in the library.

#### GroJo

##### New member
I am tutoring a kid in algebra at the local library. I found several algebra review texts in the library.
While I do appreciate the info, I need a little more then reviews. My next Problem I'm trying to solve is (x+1/x)/(1+4/2x) The video i watched on this went right to this equation after (3/4+2/5)/(1/2-1/6) <---(This one I didn't have a problem with)
They concluded that 2x was the LCD in the (x+1/x)/(1+4/2x) equation, but never showed what to factor in with exponents. The video was just like ; "Ok now lets try this one with exponents, and the LCD is 2x...yada yada without explaining what to consider with exponents or how they found the LCD to be 2x. This is always where I got lost, and simply reading a review book wont allow me to understand what I'm reading without someone saying; "Do this here", where i can reply, "duh that makes sense". Not that I expect anyone to explain it to me on here, I need a little bit more 1 on 1 for it to just 'click' in my brain.

That's why I was hoping someone might give a more creditable website, if even possible, where i can be like; "wait, i don't understand this", and I can get an educated answer. The fact I couldn't do that on this website I'm on now, has led to me to search for one where I can ask questions if i don't understand.

If anyone could answer that question though, (x+1/x)/(1+4/2x), and explain in detail how to get the answer, I know I will get it. I just understand, I can not always come to a forum every time I don't understand. That's just people doing the work for me. I am older then most people taking algebra right now, and I am not enrolled in any school, and I understand I can't simply skip learning this to keep going in school. I need to understand it, or I am just shooting myself in the foot, so to speak.

Thank you again though

I should reiterate that the method in solving (x+1/x)/(1+4/2x) was that of finding the common denominator of ALL the fractions, in order to simplify the equation. The site concluded the answer to be: x squared + 1 / x +2. Is this true?

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#### GroJo

##### New member
Not quite..pas tout a fait...in Ontario, French tongued people
are nicknamed "frogs"; a bit like Newfoundlanders = Newfies
Yeah sorry lol. I used google translate to understand what the statement was, and then used it again to translate my question. I had a feeling though that it wasn't exactly accurate, but i was none the less intrigued by the statement!

#### GroJo

##### New member
After reading a lot of other post's on here, I feel as if my questions are not worth many peoples time. My problems seem to be so simple compared to others.

None the less, any help pertaining to my earlier post in this thread would be greatly appreciated.

#### JeffM

##### Elite Member
While I do appreciate the info, I need a little more then reviews. My next Problem I'm trying to solve is (x+1/x)/(1+4/2x) The video i watched on this went right to this equation after (3/4+2/5)/(1/2-1/6) <---(This one I didn't have a problem with)
They concluded that 2x was the LCD in the (x+1/x)/(1+4/2x) equation, but never showed what to factor in with exponents. The video was just like ; "Ok now lets try this one with exponents, and the LCD is 2x...yada yada without explaining what to consider with exponents or how they found the LCD to be 2x. This is always where I got lost, and simply reading a review book wont allow me to understand what I'm reading without someone saying; "Do this here", where i can reply, "duh that makes sense". Not that I expect anyone to explain it to me on here, I need a little bit more 1 on 1 for it to just 'click' in my brain.

That's why I was hoping someone might give a more creditable website, if even possible, where i can be like; "wait, i don't understand this", and I can get an educated answer. The fact I couldn't do that on this website I'm on now, has led to me to search for one where I can ask questions if i don't understand.

If anyone could answer that question though, (x+1/x)/(1+4/2x), and explain in detail how to get the answer, I know I will get it. I just understand, I can not always come to a forum every time I don't understand. That's just people doing the work for me. I am older then most people taking algebra right now, and I am not enrolled in any school, and I understand I can't simply skip learning this to keep going in school. I need to understand it, or I am just shooting myself in the foot, so to speak.

Thank you again though

I should reiterate that the method in solving (x+1/x)/(1+4/2x) was that of finding the common denominator of ALL the fractions, in order to simplify the equation. The site concluded the answer to be: x squared + 1 / x +2. Is this true?
Couple of things

For a number of reasons, we REALLY like one problem per thread.

Second, my thought was for you to find a review book with problems and an answer key, to attempt the problems after reading the review material, and then to come here with the ones you get wrong. There is no substitute to doing problems.

Third, here is a step by step solution of the problem. Please let me know if any step confuses you.

$$\displaystyle \dfrac{x + \dfrac{1}{x}}{1 + \dfrac{4}{2x}} = \dfrac{\dfrac{x^2}{x} + \dfrac{1}{x}}{\dfrac{2x}{2x} + \dfrac{4}{2x}} = \dfrac{\dfrac{x^2 + 1}{x}}{\dfrac{2x + 4}{2x}} = \dfrac{x^2 + 1}{x} * \dfrac{2x}{2x + 4} = \dfrac{2(x^2 + 1)}{2x + 4} = \dfrac{2(x^2 + 1)}{2(x + 2)} = \dfrac{x^2 + 1}{x + 2}$$

#### GroJo

##### New member
Couple of things

For a number of reasons, we REALLY like one problem per thread.

Second, my thought was for you to find a review book with problems and an answer key, to attempt the problems after reading the review material, and then to come here with the ones you get wrong. There is no substitute to doing problems.

Third, here is a step by step solution of the problem. Please let me know if any step confuses you.

$$\displaystyle \dfrac{x + \dfrac{1}{x}}{1 + \dfrac{4}{2x}} = \dfrac{\dfrac{x^2}{x} + \dfrac{1}{x}}{\dfrac{2x}{2x} + \dfrac{4}{2x}} = \dfrac{\dfrac{x^2 + 1}{x}}{\dfrac{2x + 4}{2x}} = \dfrac{x^2 + 1}{x} * \dfrac{2x}{2x + 4} = \dfrac{2(x^2 + 1)}{2x + 4} = \dfrac{2(x^2 + 1)}{2(x + 2)} = \dfrac{x^2 + 1}{x + 2}$$
Yeah I feel stupid, and I am just going to take your advice and get a book. I have no idea were to start. I dont know how x became x squared /x and so on lol. I dont even know how you guys get the squared symbol next to a number in your responses, so I think Im gonna back out and try from the beginning again. I appreciate your patience and I understand why you guys like 1 problem per thread now. That makes sense to me atleast. Cheers Mate

#### Subhotosh Khan

##### Super Moderator
Staff member
$$\displaystyle x = x * 1 =\dfrac{x}{1} * \dfrac{x}{x} = \dfrac{x * 1}{x * x} = \dfrac{x^2}{x}$$

#### GroJo

##### New member
$$\displaystyle x = x * 1 =\frac{x}{1} * \frac{x}{x} = \frac{x^2}{x}$$
Yeah I understand that now. Might help if I brushed up on the order of operations of exponents, and if I understood the 5 main exponent properties, huh? Guess I wasn't as familiar with Algebra as I remember. Thank you lol

Whats even funnier is I knew that (x = x/1) and (1 = x/x) and it still eluded me!

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#### lookagain

##### Senior Member
I'm trying to solve is (x+1/x)/(1+4/2x)
GroJo, when you type this out horizontally, you need grouping symbols
around that second denominator, as in:

(x + 1/x)/(1 + 4/(2x))

---------------------------------------------------------------------------

Anyway, beside the point that you should have put that problem in a different
thread, let me give you an alternative solution. It has the advantage from going
from four lines of a complex fraction down to lines of a non-complex fraction.

Multiply the numerator and denominator by the least common denominator,
which is 2x.

Then factor and reduce (cancel out/divide out common factors).

$$\displaystyle \dfrac{x \ + \ \dfrac{1}{x}}{1 \ + \ \dfrac{4}{2x}} \ =$$

$$\displaystyle \dfrac{(2x)(x) \ + \ \bigg(\dfrac{1}{x}\bigg)\bigg(\dfrac{2x}{1}\bigg)}{(2x)(1) \ + \ \bigg(\dfrac{4}{2x}\bigg)\bigg(\dfrac{2x}{1}\bigg)} \ =$$

$$\displaystyle \dfrac{2x^2 \ + \ 2}{2x \ + \ 4} \ =$$

$$\displaystyle \dfrac{2(x^2 \ + \ 1)}{2(x \ + \ 2)} \ =$$

$$\displaystyle \boxed{ \ \dfrac{x^2 \ + \ 1}{x \ + \ 2} \ } \$$

#### GroJo

##### New member
Why is it i need parentheses around the 2x in this equation? What makes it different then the original equation?

#### JeffM

##### Elite Member
Why is it i need parentheses around the 2x in this equation? What makes it different then the original equation?
Because /2 means divided by 2. /(2x) means divided by 2x.

#### GroJo

##### New member
Because /2 means divided by 2. /(2x) means divided by 2x.
OK that makes sense. ty