Answer
$\dfrac{5x}{(x-6)(x-1)(x+4)}$.
Work Step by Step
Factor $x^2-7x+6$:
Rewrite $-7x$ as $-6x-1x$.
$=x^2-6x-1x+6$
Group the terms.
$=(x^2-6x)+(-1x+6)$
Factor each group.
$=x(x-6)-1(x-6)$
Factor out $(x-6)$.
$=(x-6)(x-1)$
Factor $x^2-2x-24$:
Rewrite $-2x$ as $-6x+4x$.
$=x^2-6x+4x-24$
Group the terms.
$=(x^2-6x)+(4x-24)$
Factor each group.
$=x(x-6)+4(x-6)$
Factor out $(x-6)$.
$=(x-6)(x+4)$
Thus, the given expression is eqivalent to:
$\dfrac{x}{(x-6)(x-1)}-\dfrac{x}{(x-6)(x+4)}$
The LCD is $(x-6)(x-1)(x+4)$.
Multiply numerators and denominators to form equal denominators.
$=\dfrac{x}{(x-6)(x-1)}\cdot \dfrac{x+4}{x+4}-\dfrac{x}{(x-6)(x+4)}\cdot \dfrac{x-1}{x-1}$
$=\dfrac{x(x+4)}{(x-6)(x-1)(x+4)}-\dfrac{x(x-1)}{(x-6)(x-1)(x+4)}$
Add numerators and retain the denominator.
$=\dfrac{x(x+4)-x(x-1)}{(x-6)(x-1)(x+4)}$
Use distributive property.
$=\dfrac{x^2+4x-x^2+x}{(x-6)(x-1)(x+4)}$
Simplify by combining like terms:
$=\dfrac{5x}{(x-6)(x-1)(x+4)}$
