Answer
$\dfrac{(x-9)}{(2x-1)}$
Work Step by Step
Given: $\dfrac{x^2-7x-18}{2x^2+3x-2}$
This can be factorize as:
$\dfrac{x^2-7x-18}{2x^2+3x-2}=\dfrac{x^2-9x+2x-18}{2x^2+4x-x-2}$
or, $=\dfrac{(x+2)(x-9)}{(x+2)(2x-1)}$
Hence, $=\dfrac{(x-9)}{(2x-1)}$