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Chapter 7: Q. 104 (page 668)

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.

5c2-4c+4,3cc2-7c+10

Short Answer

Expert verified

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

(b) The expressions with LCD are5(c-5)(c-2)(c-2)(c-5),3c(c-2)(c-2)(c-5).

Step by step solution

01

Part (a) Step 1. Given Information 

The given expressions are5c2-4c+4,3cc2-7c+10.

02

Part (a) Step 2. Find LCD  

  • Factor the denominators of both the given rational expressions.

c2-4c+4=(c-2)(c-2)c2-7c+10=(c-2)(c-5)

  • So, the LCD is (c-2)(c-2)(c-5).
03

Part (b) Step 1. Given Information  

The given expressions are5c2-4c+4,3cc2-7c+10

04

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.

5c2-4c+4=5(c-5)(c-2)(c-2)(c-5)3cc2-7c+10=3c(c-2)(c-2)(c-5)

  • So, the expressions with equal denominators are 5(c-5)(c-2)(c-2)(c-5),3c(c-2)(c-2)(c-5).

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