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Chapter 11: Q. 7.31 (page 1069)

Find the LCD for the expressions 2x2-x-12,1x2-16rewrite them as equivalent rational expressions with the lowest common denominator.

Short Answer

Expert verified

(a) The LCD of the rational expressions isx+4x+3x-4

(b) The required rational expressions are 2x+4x-4x+3x+4,x+3x-4x+4x+3

Step by step solution

01

Part (a) Step 1. Given information

The given rational expressions are2x2-x-12,1x2-16.

02

Part (a) Step 2. Find LCD

  • Factor the denominators of both the expressions.

x2-x-12=x-4x+3x2-16=x-4x+4

  • So, the LCD will be (x+3)x-4x+4
03

Part (b) Step 1. Given Information

The given expressions are2x2-x-12,1x2-16

04

Part (b) Step 2. Multiply by missing Factors

  • Multiply each rational expressions' numerator and denominator by the missing factor.

2x2-x-12=2x+4x-4x+3x+41x2-16=x+3x-4x+4x+3

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