Answer
$I$
Work Step by Step
Given: $\dfrac{x^2-81}{2x^2+23x+45}$
As we know $(a^2-b^2)=(a-b)(a+b)$
Thus,
$\dfrac{x^2-81}{2x^2+23x+45}=\dfrac{(x-9)(x+9)}{2x^2+18x+5x+45}$
$=\dfrac{(x-9)(x+9)}{(2x+5)(x+9)}$
$=\dfrac{(x-9)}{(2x+5)}$
Hence, the correct answer is $I$.