# Thread: Help with a fraction involving variables.

1. ## Help with a fraction involving variables.

Hello everyone, I have this problem for homework:

(a-b)/a - (a+b)/b is the numerator. The denominator is: (a-b)/b + (a+b)/a. I know the answer is supposed to be -1, but I'm not sure how to get it.

2. PLEASE rewrite this with brackets where they are needed, this is unreadable.

3. Hello, beefdawg!

$\displaystyle \text{Simplify: }\;\frac{\dfrac{a-b}{a} - \dfrac{a+b}{b}} {\dfrac{a-b}{b} + \dfrac{a+b}{a}}$

$\displaystyle \text{Multiply by }\frac{ab}{ab}\!:\;\;\frac{ab\left(\dfrac{a-b}{a} - \dfrac{a+b}{b}\right)} {ab\left(\dfrac{a-b}{b} + \dfrac{a+b}{a}\right)} \;=\;\frac{b(a-b) - a(a+b)}{a(a-b) + b(a+b)}$

. . . . . $\displaystyle =\;\frac{ab - b^2 - a^2 - ab}{a^2-ab + ab + b^2} \;=\; \frac{-a^2 - b^2}{a^2+b^2} \;=\;\frac{-(a^2+b^2)}{a^2+b^2} \;=\;-1$

4. ## Re: Help with a fraction involving variables.

Aah I see. Thank you very much for the help...just a quick question though...why exactly do we multiply both sides by ab?

5. ## Re: Help with a fraction involving variables.

It isn't necessary to multiply the fraction by ab, it probably just make it easier.

Instead, you can treat the numerator and the denominator as separate fractions, simplify then put it into one fraction