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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. 220 (page 694)

In the following exercises, solve each rational equation.
$\frac{m}{m + 5} = \frac{50}{m^{2} - 25} + 6$

Short Answer

Expert verified

The solution is $m = 4$ .

Step by step solution

01

Step 1. Given

The given equation is: $\frac{m}{m + 5} = \frac{50}{m^{2} - 25} + 6$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

The denominators can never be 0. So, $m 鈮� - 5, 5$ .

Multiply both sides by the LCD and then solve the equation.

$\frac{m}{m + 5} = \frac{50}{m^{2} - 25} + 6 \frac{m}{m + 5} = \frac{50}{(m + 5) (m - 5)} + 6 \frac{m}{m + 5} (m + 5) (m - 5) = \frac{50}{(m + 5) (m - 5)} (m + 5) (m - 5) + 6 (m + 5) (m - 5) m (m - 5) = 50 + 6 (m^{2} - 25) m^{2} - 5 m = 50 + 6 m^{2} - 150 5 m^{2} + 5 m - 100 = 0 5 (m^{2} + m - 20) = 0 5 (m + 5) (m - 4) = 0 m = - 5, 4$

But $m 鈮� - 5$ , so $m = 4$ .

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Most popular questions from this chapter

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