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Chapter 8: Q 180 (page 953)

Write as equivalent rational expression with LCD (a+9)(a+5)(a-9)of 6a2+14a+45,5aa2-81.

Short Answer

Expert verified

The result is6a-54(a+9)(a+5)(a-9),5a2+25a(a+9)(a-9)(a+5).

Step by step solution

01

Given Information

The given expression is6a2+14a+45,5aa2-81

The LCD is(a+9)(a+5)(a-9).

02

Factor the denominator of both expressions.

The factored form of first denominator.

a2+14a+45=(a+9)(a+5)

The factored form of second denominator.

a2-81=(a+9)(a-9)

The fractions in factored form is6(a+9)(a+5),5a(a+9)(a-9).

03

Multiply each denominator by the 'missing' factor and multiplyeach numerator by the same factor.

6(a-9)(a+9)(a+5)(a-9),5a(a+5)(a+9)(a-9)(a+5)

04

Simplify the numerators.

Multiply the numerator using distributive property.

6a-54(a+9)(a+5)(a-9),5a2+25a(a+9)(a-9)(a+5)

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