Answer
$\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}=\dfrac{1}{x-6}$
Work Step by Step
$\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}$
Evaluate the substraction of the two rational expressions:
$\dfrac{2x+3}{x^{2}-x-30}-\dfrac{x-2}{x^{2}-x-30}=\dfrac{2x+3-x+2}{x^{2}-x-30}=...$
$...=\dfrac{x+5}{x^{2}-x-30}=...$
Factor the denominator and then, simplify:
$...=\dfrac{x+5}{(x-6)(x+5)}=\dfrac{1}{x-6}$
