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Chapter 8: Q. 337 (page 982)

In the following exercises, solve.

nn+2=8n2-4+3

Short Answer

Expert verified

The solution isn=1,-2

Step by step solution

01

Step 1. Given Information

The rational equation is given as:

nn+2=8n2-4+3

02

Step 2. Least Common Denominator(LCD)

The LCD of the equation is (n+2)(n-2)

Multiply the equation by the LCD,

(n+2)(n-2)nn+2=8n2-4+3(n+2)(n-2)n(n-2)=8+3(n+2)(n-2)n2-2n=8+3(n2-4)n2-2n=8+3n2-122n2+2n-4=02(n2+n-2)=0

03

Step 3. Solution of the equation

The equation can be factored as,

2(n2+n-2)=02(n2+2n-n-2)=02(n+2)(n-1)=0

Using the Zero product property,

n+2=0,n-1=0n=-2,n=1.

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