Question

Simplify: 2x^2 + 19x + 35/2x^2 +11x +15 a) 7/3b) 19x + 35/11x + 15c) 2x + 7/2x + 3d) x + 7/x + 3

Answer 1

We want to simplify

`\frac{2x^2+19x+35}{2x^2+11x+15\text{ }}`

Factorising the numerator and denominator, we have

`\begin{gathered} \frac{2x^2+19x+35}{2x^2+11x+15\text{ }} \\ \frac{2x^2+14x+5x+35}{2x^2+6x+5x+15\text{ }} \\ (2x(x+7)+5(x+7))/(2x(x+3)+5(x+3)) \\ ((2x+5)(x+7))/((2x+5)(x+3)) \end{gathered}`

Canceling out the common factor which is

`2x+5`

We have our answer as

`(x+7)/(x+3)`

Hence the answer is option D