Answer
$\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}=\dfrac{1}{x-1}$
Work Step by Step
$\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}$
Evaluate the substraction of the two rational expressions:
$\dfrac{3x-1}{x^{2}+5x-6}-\dfrac{2x-7}{x^{2}+5x-6}=\dfrac{(3x-1)-(2x-7)}{x^{2}+5x-6}=...$
$...=\dfrac{3x-1-2x+7}{x^{2}+5x-6}=\dfrac{x+6}{x^{2}+5x-6}=...$
Factor the denominator and simplify:
$...=\dfrac{x+6}{(x+6)(x-1)}=\dfrac{1}{x-1}$
