I'm stuck on this question! Please help me!

[Tadams052012]

Hi there, I'm new to this forum. I'm self studying Algebra from a book called Teach Yourself Algebra - A Complete Introduction, in preparation for an Access to Higher Education course I'll be enrolling on next year, and I'm stuck on this question -

x + 4
3x

Now I normally have no problem adding fractions but this is algebra and so makes things a little more complicated in my mind.

If the question was non algebraic I would proceed as follows, for example -

28 + 2
3

In this case I would convert the whole number 28 into fraction form as follows -

28 + 2
1 3

I would then proceed with the normal process for adding fractions.

The problem I'm having with the initial algebraic question I posted above is that I keep getting -

3x + 4
3x

Unfortunately the book tells me that the answer should be -

3x² + 4
3x

Could anyone take me through the correct way to tackle this problem in a step by step manner, and perhaps suggest where I might be going wrong?

I can post my full workings if necessary. Thank you for your patience as I know this is quite a simple problem.

Tom.

---

 

[Dr.Peterson]

Hi there, I'm new to this forum. I'm self studying Algebra from a book called Teach Yourself Algebra - A Complete Introduction, in preparation for an Access to Higher Education course I'll be enrolling on next year, and I'm stuck on this question -

x + 4
3x

Now I normally have no problem adding fractions but this is algebra and so makes things a little more complicated in my mind.

If the question was non algebraic I would proceed as follows, for example -

28 + 2
3

In this case I would convert the whole number 28 into fraction form as follows -

28 + 2
1 3

I would then proceed with the normal process for adding fractions.

The problem I'm having with the initial algebraic question I posted above is that I keep getting -

3x + 4
3x

Unfortunately the book tells me that the answer should be -

3x² + 4
3x

Could anyone take me through the correct way to tackle this problem in a step by step manner, and perhaps suggest where I might be going wrong?

I can post my full workings if necessary. Thank you for your patience as I know this is quite a simple problem.

Tom.

---

You want to simplify x + 4/(3x), that is, \(\displaystyle x+\dfrac{4}{3x}\).

As you say, you can write this as x/1 + 4/(3x). Now you have to express the first fraction using 3x as its denominator; so you have to multiply numerator and denominator by 3x: (3x*x)/(3x*1 + 4/(3x) = (3x²)/(3x) + 4/(3x) = (3x^2 + 4)/3x.

I'm not sure where you went wrong, but I think you may just not have written out each step.

Here it is more readably; I typed it out above to show how to write clearly without knowing the fancy typography:

\(\displaystyle \dfrac{x}{1} + \dfrac{4}{3x} = \dfrac{x\cdot 3x}{1\cdot3x} + \dfrac{4}{3x} = \dfrac{3x^2}{3x} + \dfrac{4}{3x} = \dfrac{3x^2+4}{3x}\)

 

[JeffM]

First, please read
https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=436773#post436773

Second, your first three posts will be moderated. That means there will be a delay in your posts appearing.

Third, please show fractions and division as a / b. The way you have written this problem is very unclear.

\(\displaystyle x + \dfrac{4}{3x}\) should be written out as x + 4 / (3x). PEMDAS

\(\displaystyle x + \dfrac{4}{3x} = \dfrac{x}{1}. + \dfrac{4}{3x}.\)

Correct first step. You add fractions by getting identical denominators and then adding numerators. But for any real number r

\(\displaystyle r \equiv \dfrac{r}{1}.\)

So if you have a number without a denominator, you can always give it a denominator of 1.

But is 1 the same as 3x? Well, x is a number that we do not know yet so there is no way to tell. And you can't add those fractions until you are certain that the denominators are the same. However for any real numbers r and s, s not equal to zero,

\(\displaystyle r \equiv \dfrac{r}{1} \equiv \dfrac{r}{1} * 1 \equiv \dfrac{r}{1} * \dfrac{s}{s} \equiv \dfrac{rs}{s}.\)

The way we make \(\displaystyle \dfrac{x}{1}\) into an equivalent fraction with 3x as a denominator is to multiply as follows

\(\displaystyle \dfrac{x}{1} * \dfrac{3x}{3x} = \dfrac{x * 3x}{1 * 3x} = \dfrac{3x^2}{3x}.\).

Putting this altogether

\(\displaystyle x + \dfrac{4}{3x} = \dfrac{x}{1} + \dfrac{4}{3x} = \\

\left ( \dfrac{x}{1} * \dfrac{3x}{3x} \right ) + \dfrac{4}{3x} = \dfrac{3x^2}{3x} + \dfrac{4}{3x} = \dfrac{3x^2 + 4}{3x}.\)

 

[sinx]

Hi there, I'm new to this forum. I'm self studying Algebra from a book called Teach Yourself Algebra - A Complete Introduction, in preparation for an Access to Higher Education course I'll be enrolling on next year, and I'm stuck on this question -

x + 4
3x

The problem I'm having with the initial algebraic question I posted above is that I keep getting -

3x + 4
3x

Unfortunately the book tells me that the answer should be -

3x² + 4
3x

Could anyone take me through the correct way to tackle this problem in a step by step manner, and perhaps suggest where I might be going wrong?

Tom.

---

the other answers are more complete, but this may help;
in order to add x to 4/(3x), the x has to also have a 3x denominator
to get 3x in the denominator, you have to multiply by 1, i.e. 3x/3x.
this converts x/1 to 3x²/3x;
[they are the same, just different form.]

the key is multiplying by 1.

 

[Denis]

Take a simple example:

3/4 + 2

= 3/4 + 8/4

= 11/4

Follow that?

 

[Tadams052012]

Thank you all for your patience and for your help. I see where I went wrong now (I see where the 3x² comes from) and feel I have a better understanding of this kind of question. I apologize for my unclear posting format, this is something I will certainly make sure I get right should I feel the need to consult this forum again in the future.

Again I cannot thank you enough. Helping someone with a mathematics problem may seem like a small thing, but ultimately little pieces of help like this could mean the difference between me getting up to speed for my course, passing my course, getting into University, succeeding at University, getting a well paid job and being able to start a family in the future. In short, whilst it feels a little corny to say it, little bits of help like this can make a big difference.

Kind regards,
Tom.