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