Answer
$\frac{x^2-14x-16}{(x+6)(x-2)}$.
Work Step by Step
The given expression is
$=\frac{2x-1}{x+6}-\frac{x+3}{x-2}$
LCM of all the denominators $=(x+6)(x-2)$
$=\frac{(x-2)}{(x-2)} \cdot \frac{2x-1}{x+6}-\frac{(x+6)}{(x+6)} \cdot \frac{x+3}{x-2}$
Simplify.
$=\frac{(2x-1)(x-2)}{(x+6)(x-2)}- \frac{(x+6)(x+3)}{(x+6)(x-2)}$
$=\frac{(2x-1)(x-2)-(x+6)(x+3)}{(x+6)(x-2)}$
Use the distributive property.
$=\frac{2x^2-x-4x+2-[x^2+3x+6x+18]}{x^2+6x-2x-12}$
Simplify.
$=\frac{2x^2-x-4x+2-x^2-3x-6x-18}{x^2+6x-2x-12}$
$=\frac{x^2-14x-16}{x^2+4x-12}$
Factor the denominator $x^2+4x-12$.
$=x^2+6x-2x-12$
$=(x^2+6x)+(-2x-12)$
$=x(x+6)-2(x+6)$
$=(x+6)(x-2)$
Substitute the factor.
$=\frac{x^2-14x-16}{(x+6)(x-2)}$.
