Question

What is the sum? exFormula1" title=" \frac{3}{x^-9} + \frac{5}{x+3} " alt=" \frac{3}{x^-9} + \frac{5}{x+3} " align="absmiddle" class="latex-formula">

Answer 1

Make denomenators the same

times left denomenator by (x+3)/(x+3) and right one by (x-9)/(x-9)

$\frac{3(x+3)}{(x-9)(x+3)}+ \frac{5(x-9)}{(x-9)(x+3)}$=
$\frac{3(x+3)+5(x-9)}{(x-9)(x+3)}$=
$\frac{3x+9+5x-45}{(x-9)(x+3)}$=
$\frac{8x-36}{(x-9)(x+3)}$

if expandded we get
$\frac{8x-36}{x^2-6x-27}$