Chapter 8: Q 8.98 (page 953)

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

Short Answer

Expert verified

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

Step by step solution

Given information

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

Factor denominator

$= \frac{3 w}{w + 2} + \frac{2}{w + 7} - \frac{17 w + 4}{w^{2} + 9 w + 14} = \frac{3 w}{w + 2} + \frac{2}{w + 7} - \frac{17 w + 4}{w^{2} + 7 w + 2 w + 14} - = \frac{3 w}{w + 2} + \frac{2}{w + 7} - \frac{17 w + 4}{(w + 2) (w + 7)}$

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

Common denominator

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

Simplify

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

Short Answer

Step by step solution

Given information

Factor denominator

Common denominator

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Simplify: 3ww+2+2w+7-17w+4w2+9w+14

Short Answer

Step by step solution

Given information

Factor denominator

Common denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Calculus

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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