Answer
$\dfrac{x^2(4x-15)}{(2x-5)^2}$
Work Step by Step
Use distributive property.
$\dfrac{(2x-5)\cdot 3x^2-x^3\cdot 2}{(2x-5)^2}\\
=\dfrac{6x^3-15x^2-2x^3}{(2x-5)^2}$
Simplify by combining lke terms.
$=\dfrac{4x^3-15x^2}{(2x-5)^2}$
Factor the numerator.
$=\dfrac{x^2(4x-15)}{(2x-5)^2}$
The numerator and the denominator have no common factors. Hence, the lowest term is $\dfrac{x^2(4x-15)}{(2x-5)^2}$.
