SOLUTION
We want to simplify
[tex]\frac{2x^2+19x+35}{2x^2+11x+15\text{ }}[/tex]Factorising the numerator and denominator, we have
[tex]\begin{gathered} \frac{2x^2+19x+35}{2x^2+11x+15\text{ }} \\ \frac{2x^2+14x+5x+35}{2x^2+6x+5x+15\text{ }} \\ \frac{2x(x+7)+5(x+7)}{2x(x+3)+5(x+3)} \\ \frac{(2x+5)(x+7)}{(2x+5)(x+3)} \end{gathered}[/tex]Canceling out the common factor which is
[tex]2x+5[/tex]We have our answer as
[tex]\frac{x+7}{x+3}[/tex]Hence the answer is option D
