Solution
[tex]\begin{gathered} f(x)=4x^2+6x \\ g(x)=2x^2+13x+15 \end{gathered}[/tex]
Now
[tex](\frac{f}{g}_{})(x)\text{ we are going to divide}[/tex][tex](\frac{f}{g})(x)=\frac{4x^2+6x}{2x^2+13x+15}[/tex][tex]\frac{4x^2+6x}{2x^2+13x+15}=\frac{2x(2x+3)}{2x^2+13x+15}[/tex]
Now also factor the denominator
[tex]\frac{2x(2x+3)}{2x^2+13x+15}=\frac{2x(2x+3)}{(2x+3)(x+5)}[/tex]
Cancel the common factor 2x+3
[tex]=\frac{2x}{(x+5)}[/tex]
The final answer
[tex](\frac{f}{g})(x)=\frac{2x}{x+5}[/tex]
