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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 214 (page 694)

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

Short Answer

Expert verified

There is no solution.

Step by step solution

01

Step 1. Given

The given equation is: $\frac{w + 8}{w^{2} - 11 w + 28} = \frac{5}{w - 7} + \frac{2}{w - 4}$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

The denominators can never be 0. So, $w 鈮� 7, 4$ .

We multiply both sides by the LCD, then solve the linear equation.

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

But $w 鈮� 7$ . Hence, there is no solution.

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