Answer
$ \frac{4-x}{5x-3}$.
Work Step by Step
The given expression is
$=\frac{12x^{-2}-3x^{-1}}{15x^{-1}-9x^{-2}}$
Multiply the numerator and the denominator by $x^{2}$.
$=\frac{x^2}{x^2}\cdot \frac{12x^{-2}-3x^{-1}}{15x^{-1}-9x^{-2}}$
Use the distributive property.
$= \frac{x^2(12x^{-2})-x^2(3x^{-1})}{x^2(15x^{-1})-x^2(9x^{-2})}$
Simplify.
$= \frac{12x^{-2+2}-3x^{-1+2}}{15x^{-1+2}-9x^{-2+2}}$
$= \frac{12x^{0}-3x^{1}}{15x^{1}-9x^{0}}$
$= \frac{12-3x}{15x-9}$
Factor out $3$ from the numerator and denominator.
$= \frac{3(4-x)}{3(5x-3)}$
Simplify.
$= \frac{4-x}{5x-3}$.
