Answer
$3x+2$.
Work Step by Step
The given expression is
$=\frac{4x^2-11x+4}{x-3}-\frac{x^2-4x+10}{x-3}$
$=\frac{4x^2-11x+4-(x^2-4x+10)}{x-3}$
Clear the parentheses.
$=\frac{4x^2-11x+4-x^2+4x-10}{x-3}$
Add like terms.
$=\frac{3x^2-7x-6}{x-3}$
Factor $3x^2-7x-6$.
Rewrite the middle term $-7x$ as $-9x+2x$
$=3x^2-9x+2x-6$
Group terms.
$=(3x^2-9x)+(2x-6)$
Factor each term.
$=3x(x-3)+2(x-3)$
Factor out $(x-3)$.
$=(x-3)(3x+2)$.
Substitute the factor into the fraction
$=\frac{(x-3)(3x+2)}{x-3}$
Cancel common terms
$=3x+2$.
