Chapter 8: Q. 328 (page 982)

In the following exercises, solve.
$\frac{w + 8}{w^{2} - 11 w + 28} = \frac{5}{w - 7} + \frac{2}{w - 4}$

Short Answer

Expert verified

The solution is $w = 7 .$

Step by step solution

Step 1. Given Information

The given rational expression is :

$\frac{w + 8}{w^{2} - 11 w + 28} = \frac{5}{w - 7} + \frac{2}{w - 4}$

Step 2. Removing the fraction

The least common denominator is $(w - 7) (w - 4)$

Multiply the equation by the LCD,

$(w - 7) (w - 4) \frac{w + 8}{w^{2} - 11 w + 28} = [\frac{5}{w - 7} + \frac{2}{w - 4}] (w - 7) (w - 4) w^{2} - 11 w + 28 \times \frac{w + 8}{w^{2} - 11 w + 28} = [5 (w - 4) + 2 (w - 7)] w + 8 = 5 w - 20 + 2 w - 14 w + 8 = 7 w - 34 6 w = 42 w = 7$

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In the following exercises, solve.
$\frac{w + 8}{w^{2} - 11 w + 28} = \frac{5}{w - 7} + \frac{2}{w - 4}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Removing the fraction

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In the following exercises, solve.w+8w2-11w+28=5w-7+2w-4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Removing the fraction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{w + 8}{w^{2} - 11 w + 28} = \frac{5}{w - 7} + \frac{2}{w - 4}$