Answer
$\frac{2a^2+21ab-10b^2}{(a-b)(a+2b)(a+6b)}$.
Work Step by Step
Factor each term of the given expression.
$\frac{5a-b}{a^2+ab-2b^2}-\frac{3a+2b}{a^2+5ab-6b^2}=\frac{5a-b}{(a+2b)(a-b)}-\frac{3a+2b}{(a+6b)(a-b)}$
LCD is $=(a-b)(a+2b)(a+6b)$.
Multiply each numerator and denominator by the extra factor required to form the LCD.
$=\frac{5a-b}{(a+2b)(a-b)}\times \frac{(a+6b)}{(a+6b)}-\frac{3a+2b}{(a+6b)(a-b)}\times \frac{(a+2b)}{(a+2b)}$
Simplify.
$=\frac{(5a-b)(a+6b)}{(a-b)(a+2b)(a+6b)}-\frac{(3a+2b)(a+2b)}{(a-b)(a+2b)(a+6b)}$
Add both numerators.
$=\frac{(5a-b)(a+6b)-(3a+2b)(a+2b)}{(a-b)(a+2b)(a+6b)}$
Use the distributive property.
$=\frac{5a^2+30ab-ab-6b^2-3a^2-6ab-2ab-4b^2}{(a-b)(a+2b)(a+6b)}$
Simplify.
$=\frac{2a^2+21ab-10b^2}{(a-b)(a+2b)(a+6b)}$.
