Question

Simplify: $\frac{3w}{w+2}+\frac{2}{w+7}-\frac{17w+4}{w^2+9w+14}$

Short answer

The simplification of the expression is$\frac{3w}{w+7}$.

Step-by-step solution

Given information

The given rational expression is$\frac{3w}{w+2}+\frac{2}{w+7}-\frac{17w+4}{w^2+9w+14}$

Factor denominator

$$\begin{gathered} =\frac{3w}{w+2}+\frac{2}{w+7}-\frac{17w+4}{w^2+9w+14} \\ =\frac{3w}{w+2}+\frac{2}{w+7}-\frac{17w+4}{w^2+7w+2w+14}- \\ =\frac{3w}{w+2}+\frac{2}{w+7}-\frac{17w+4}{\left(w+2\right)\left(w+7\right)} \end{gathered}$$

The LCD of the expression is $\left(w+2\right)\left(w+7\right)$.

Common denominator

Rewrite each rational expression as an equivalent rational expression with the LCD.

Simplify