Question

A           B
------ - ------ = ???
a-b      a+b

Answer 1

$\frac{a}{a - b} - \frac{b}{a + b}$

$= \frac{a(a + b)}{(a + b)(a - b)} - \frac{b(a - b)}{(a + b)(a - b)}$

$= \frac{a(a + b) - b(a - b)}{(a - b)(a + b)}$

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

$= \frac{ {a}^{2} + {b}^{2} }{ {a}^{2} - {b}^{2} }$