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Chapter 7: Q. 420 (page 736)

In the following exercises, perform the indicated operations

nn+3+2n-3-n-9n2-9

Short Answer

Expert verified

The simplified expression isn-5n-3

Step by step solution

01

Step 1. Given information

Expression:

nn+3+2n-3-n-9n2-9

02

Step 2. Find LCD     

Denominator of the first fraction is n+3

Denominator of the second fraction is n-3

Denominator of the third fraction isn2-9

It can be factorize as

n2-9=n2-32=(n-3)(n+3)

So LCD isn-3n+3

03

Step 3. Rewrite each rational expression as  an equivalent rational expression with the LCD      

n(n-3)(n+3)(n-3)+2(n+3)(n-3)(n+3)-n-9(n-3)(n+3)

04

Step 4.Simplify the numerators and perform operations

(n2-3n)(n+3)(n-3)+(2n+6)(n+3)(n-3)-(n-9)(n+3)(n-3)=(n2-3n)+(2n+6)-(n-9)(n+3)(n-3)=n2-3n+2n+6-n+9(n+3)(n-3)

05

Step 5. Simplify numerators

n2-2n+15(n+3)(n-3)

06

Step 6. factorize numerator

n2-5n+3n+15(n+3)(n-3)=n(n-5)+3(n-5)(n+3)(n-3)=(n-5)(n+3)(n+3)(n-3)

07

Step 7. Cancel common factors

n-5n-3

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