#### Answer

$\dfrac{x^{2}+7x+10}{x-1}\div\dfrac{x^{2}+2x-15}{x-1}=\dfrac{x+2}{x-3}$

#### Work Step by Step

$\dfrac{x^{2}+7x+10}{x-1}\div\dfrac{x^{2}+2x-15}{x-1}$
Factor the numerators of both fractions:
$\dfrac{(x+5)(x+2)}{x-1}\div\dfrac{(x+5)(x-3)}{x-1}=...$
Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator of the resulting expression:
$...=\dfrac{(x-1)(x+5)(x+2)}{(x-1)(x+5)(x-3)}=\dfrac{x+2}{x-3}$