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Q. 104

Expert-verified

Intermediate Algebra

Found in: Page 668

Book edition OER 2017

Author(s) OPENSTAX

Pages 1346 pages

ISBN 9780998625720

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Short Answer

In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator.
$\frac{5}{c^{2} - 4 c + 4}, \frac{3 c}{c^{2} - 7 c + 10}$

(a) The LCD is $(c - 2) (c - 2) (c - 5)$ .

(b) The expressions with LCD are $\frac{5 (c - 5)}{(c - 2) (c - 2) (c - 5)}, \frac{3 c}{(c - 2) (c - 2) (c - 5)}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1. Given Information

The given expressions are $\frac{5}{c^{2} - 4 c + 4}, \frac{3 c}{c^{2} - 7 c + 10}$ .

Part (a) Step 2. Find LCD

Factor the denominators of both the given rational expressions.

$c^{2} - 4 c + 4 = (c - 2) (c - 2) c^{2} - 7 c + 10 = (c - 2) (c - 5)$

So, the LCD is $(c - 2) (c - 2) (c - 5)$ .

Part (b) Step 1. Given Information

The given expressions are $\frac{5}{c^{2} - 4 c + 4}, \frac{3 c}{c^{2} - 7 c + 10}$

Part (b) Step 2. Express the expressions with LCD

Multiply and divide the expressions by the missing factor to make the denominator equal to LCD.

$\frac{5}{c^{2} - 4 c + 4} = \frac{5 (c - 5)}{(c - 2) (c - 2) (c - 5)} \frac{3 c}{c^{2} - 7 c + 10} = \frac{3 c}{(c - 2) (c - 2) (c - 5)}$

So, the expressions with equal denominators are $\frac{5 (c - 5)}{(c - 2) (c - 2) (c - 5)}, \frac{3 c}{(c - 2) (c - 2) (c - 5)}$ .

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