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Chapter 7: Q. 100 (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.

8y2+12y+35,3yy2+y-42

Short Answer

Expert verified

(a) The LCD is y+5y-6y+7.

(b) The expressions with LCD are8y-6y+5y-6y+7,3yy+5y+5y-6y+7.

Step by step solution

01

Part (a) Step 1. Given Information

The given expressions are8y2+12y+35,3yy2+y-42.

02

Part (a) Step 2. Find LCD 

  • Factor the denominators of both the given rational expressions.

y2+12y+35=y+7y+5y2+y-42=y+7y-6

  • So, the LCD isy+5y-6y+7.
03

Part (b) Step 1. Given Information

The given expressions are8y2+12y+35,3yy2+y-42.

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.

8y2+12y+35=8y-6y+5y-6y+73yy2+y-42=3yy+5y+5y-6y+7

  • So, the expressions with equal denominators are8y-6y+5y-6y+7,3yy+5y+5y-6y+7.

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