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Chapter 7: Q. 414 (page 736)

In the following exercises, perform the indicated operations

3xx2-9+5x2+6x+9

Short Answer

Expert verified

The simplified expression is3x2+14x-15(x+3)2(x-3)

Step by step solution

01

Step 1. Given information

Expression :

3xx2-9+5x2+6x+9
02

Step 2. Find LCD  

Denominator of first fraction isx2-9

Factorize this denominator

x2-32=(x-3)(x+3)

Denominator of the second fraction isx2+6x+9

Factorize this denominator

x2+2.3.x+32=(x+3)2

here x+3is common between both denominator

So the LCD isx+32x-3

03

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

3x(x+3)(x+3)2(x-3)+5(x-3)(x+3)2(x-3)

04

Step 4.Simplify the numerators.   

3x2+9x(x+3)2(x-3)+5x-15(x+3)2(x-3)

05

Step 5. Add numerators of the fractions   

3x2+9x+5x-15(x+3)2(x-3)

06

Step 6. Simplify numerator 

3x2+14x-15(x+3)2(x-3)

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