Algebra fraction within a fraction

jmiller634

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Aug 25, 2011
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I am taking algebra at my college and the teacher is very hard to learn from, for me anyway. He has assigned this problem: x/(x-(x+1)/2)=4
I have tried for hours to get the right answer that matches the book's answer, but I can't get it :(
Any help would be greatly appreciated.
 
Before proceeding, let me make sure that I have the problem right.

Solve the equation: \(\displaystyle \dfrac{x}{x - \frac{x + 1}{2}} = 4\)

Is that what you are being asked to solve?

Yes, this is my first time using this site do I don't know how to draw it like you did. What you wrote is exactly how it looks in my math book.
 
Hello, jmiller634!

Solve the equation: \(\displaystyle \dfrac{x}{x - \frac{x + 1}{2}} = 4\)

Multiply the left side by \(\displaystyle \frac{2}{2}\!:\)

. . \(\displaystyle \dfrac{2}{2}\cdot\dfrac{x}{x-\frac{x+1}{2}} \:=\:4 \quad\Rightarrow\quad \dfrac{2x}{2x - (x+1)} \:=\:4 \)

. . \(\displaystyle \dfrac{2x}{2x-x-1} \:=\:4 \quad\Rightarrow\quad \dfrac{2x}{x-1} \:=\:4\)


Can you finish it now?
 
Don't worry: you wrote it properly using grouping symbols. I wanted to check because many students when they first come here are a bit sketchy about grouping symbols.

OK Here is the GENERAL method to SIMPLIFY algebraic fractions.

In this problem you have a denominator that is partly a fraction and partly not a fraction. If you have such a beast in either numerator or denominator or both, turn both the numerator and denominator into pure fractions as a FIRST step. In the case of your problem, you have this mixed form in the denominator so you need to turn both numerator and denominator into pure fractions.

What is the denominator in pure fractional form?
What is the numerator in pure fractional form?

The SECOND step is to turn the division into multiplication through the following identity \(\displaystyle \dfrac{\frac{a}{b}}{\frac{c}{d}} = \dfrac{a}{b} * \dfrac{d}{c}\). In other words you turn one complicated fraction into the product of two simpler fractions.

What two fractions to multiply together do you end up with from the fraction resulting from step 1?

The THIRD step is to cancel any FACTORS that appear in both a numerator and a denominator. In this case, you do not have any such factors so you can ignore this step, but it is an important part of the general method.

The FOURTH step is to do whatever multiplications are necessary to form a single fraction.

Your problem has now been SIMPLIFIED to the form \(\displaystyle \dfrac{e}{f} = 4\).

What do you do next?

is this what you mean by pure fractions in the numerator and denominator? x/1 over x/1 - x/2 + 1/2 = 4?
 
Hello, jmiller634!


Multiply the left side by \(\displaystyle \frac{2}{2}\!:\)

. . \(\displaystyle \dfrac{2}{2}\cdot\dfrac{x}{x-\frac{x+1}{2}} \:=\:4 \quad\Rightarrow\quad \dfrac{2x}{2x - (x+1)} \:=\:4 \)

. . \(\displaystyle \dfrac{2x}{2x-x-1} \:=\:4 \quad\Rightarrow\quad \dfrac{2x}{x-1} \:=\:4\)


Can you finish it now?
yes I get x=2, but how come you could multiply the left side of the equation by 2/2 but not have to multiply the right side (the 4) by 2/2? I thought that whatever you did to one side, you had to do to the other side?
 
Ty all guys, I finally got it. Ty for the fast, spot on responses. I will probably be back with more questions lol.
 
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