Answer
$\frac{x+9}{x+3}$
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:
$\frac{7x^{2}+61x-18}{7x^{2}+19x-6}$
=$\frac{7x^{2}-2x+63x-18}{7x^{2}-2x+21x-6}$
=$\frac{x(7x-2)+9(7x-2)}{x(7x-2)+3(7x-2)}$
=$\frac{(7x-2)(x+9)}{(7x-2)(x+3)}$
=$\frac{x+9}{x+3}$
