#### Answer

$\dfrac{5x^{2}+4x}{x-1}-\dfrac{6x+3}{x-1}=5x+3$

#### Work Step by Step

$\dfrac{5x^{2}+4x}{x-1}-\dfrac{6x+3}{x-1}$
Evaluate the substraction of the two rational expressions:
$\dfrac{5x^{2}+4x}{x-1}-\dfrac{6x+3}{x-1}=\dfrac{(5x^{2}+4x)-(6x+3)}{x-1}=...$
$...=\dfrac{5x^{2}+4x-6x-3}{x-1}=\dfrac{5x^{2}-2x-3}{x-1}=...$
Factor the numerator and simplify:
$...=\dfrac{(5x+3)(x-1)}{x-1}=5x+3$