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Chapter 8: Q. 72 (page 919)

Explain all the steps you take to simplify the rational expression p2+4p鈭�219鈭�p2.

Short Answer

Expert verified

p2+4p鈭�219鈭�p2=-p+7p+3

Step by step solution

01

Step 1. Given information.

We have been given a rational expression p2+4p鈭�219鈭�p2.

We have to explain all the steps taken to simplify the rational expression

02

Step 2. Factor the numerator of the given rational expression

Numerator is p2+4p鈭�21.

p2+4p鈭�21=p2+7p-3p鈭�21=p(p+7)-3(p+7)=(p-3)(p+7)

03

Step 2. Factor the denominator of the given rational expression

The denominator is 9-p2.

9-p2=32-p2=(3-p)(3+p)(Usingformulaa2-b2=(a+b)(a-b))

04

Step 4. Rewrite the rational expression with factors and cancel the common factors

p2+4p鈭�219鈭�p2=(p-3)(p+7)(3+p)(3-p)=-(3-p)(p+7)(3+p)(3-p)=-p+7p+3

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