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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. 217 (page 694)

In the following exercises, solve each rational equation.
$\frac{b + 3}{3 b} + \frac{b}{24} = \frac{1}{b}$ .

Short Answer

Expert verified

The solution is $b = - 8$ .

Step by step solution

01

Step 1. Given

The given equation is: $\frac{b + 3}{3 b} + \frac{b}{24} = \frac{1}{b}$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

The denominators can never be 0. So, $b 鈮� 0$ .

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

$\frac{b + 3}{3 b} + \frac{b}{24} = \frac{1}{b} \frac{b + 3}{3 b} (24 b) + \frac{b}{24} (24 b) = \frac{1}{b} (24 b) (b + 3) (8) + b (b) = 24 8 b + 24 + b^{2} = 24 b^{2} + 8 b = 0 b (b + 8) = 0 b = 0, - 8$

But $b 鈮� 0$ , so $b = - 8$ .

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