Originally Posted by

**TriForce** This problem is driving me nuts... it should be rather easy but...

$\displaystyle \dfrac{\dfrac{1}{a}-\dfrac{1}{a+b}}{\dfrac{1}{b}-\dfrac{1}{a+b}} = $

$\displaystyle \dfrac{\dfrac{\dfrac{b}{a}}{a+b}}{\dfrac{\dfrac{a} {b}}{a+b}}} = $

$\displaystyle \dfrac{\dfrac{b}{a}}{a+b}*\dfrac{a+b}{\dfrac{a}{b} }=$

$\displaystyle \dfrac{\dfrac{b}{a}*(a+b)}{(a+b)*\dfrac{a}{b}}=$

Think the above is correct, but not the following:

$\displaystyle \dfrac{\dfrac{ab+{b}^{2}}{a}}{\dfrac{ab+{a}^{2}}{a }}=$

$\displaystyle \frac{ab+{b}^{2}}{a}*\frac{a}{ab+{a}^{2}}=$

$\displaystyle \frac{{a}^{2}b+a{b}^{2}}{{a}^{2}b+{a}^{3}}=$

$\displaystyle \dfrac{ab+{b}^{2}}{ab+{a}^{2}}$ which is not correct the answer should be $\displaystyle \dfrac{{b}^{2}}{{a}^{2}}$