Answer
$\dfrac{-2(x^2-5x-9)}{(x^2+9)^2}$
Work Step by Step
Use distributive property.
$\dfrac{(x^2+9)\cdot 2-(2x-5)\cdot 2x}{(x^2+9)^2}\\
=\dfrac{2x^2+18-(4x^2-10x)}{(x^2+9)^2}\\
=\dfrac{2x^2+18-4x^2+10x}{(x^2+9)^2}$
Simplify by combining like terms.
$=\dfrac{-2x^2+10x+18}{(x^2+9)^2}$
Factor the numerator by factoring out $-2$.
$=\dfrac{-2(x^2-5x-9)}{(x^2+9)^2}$
The numerator can no longer be factored further.
Hence, the lowest term is $\dfrac{-2(x^2-5x-9)}{(x^2+9)^2}$.
