Answer
$\frac{2x+7}{3x+4}$
Work Step by Step
Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{2x^{2}+17x+35}{3x^{2}+19x+20}$
=$\frac{2x^{2}+7x+10x+35}{3x^{2}+4x+15x+20}$
=$\frac{x(2x+7)+5(2x+7)}{x(3x+4)+5(3x+4)}$
=$\frac{(2x+7)(x+5)}{(3x+4)(x+5)}$
=$\frac{2x+7}{3x+4}$
