Question

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

Answer 1

$f(x)=4x^2+6x=2x(2x+3)\\\\g(x)=2x^2+13x+15=2x^2+10x+3x+15=2x(x+5)+3(x+5)=(x+5)(2x+3)$

$\left(\dfrac{f}{g}\right)(x)=\dfrac{4x^2+6x}{2x^2+13x+15}=\dfrac{2x(2x+3)}{(x+5)(2x+3)}=\dfrac{2x}{x+5}$