Question

Given f(x)=4x^2+6x and g(x)=2x^2+13x+15, find (f/g)(x). Show your work.

Answer 1

(f/g)(x)= (4x^2+6x)/(2x^2+13x+15)

first simplify expression and write 13x as a sum to make easier factorization

(4x^2+6x)/(2x^2+10x+3x+15)

then factorize numerator and denominator
 
(2x(2x+3))/(2x(x+5) + 3(x+5))

rewrite and factor out denominator
(2x(2x+3))/((2x+3)(x+5))

reduce fraction
2x/(x+5)
hope that help you out