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Chapter 8: Q 181 (page 953)

Write as equivalent rational expression with LCD(b+3)(b+3)(b-5)of4b2+6b+9,2bb2-2b-15.

Short Answer

Expert verified

The result is4b-20(b+3)(b+3)(b-5),2b2+6b(b+3)(b+3)(b-5).

Step by step solution

01

Given Information

The given expression is4b2+6b+9,2bb2-2b-15.

The LCD is(b+3)(b+3)(b-5).

02

Factor the denominator of both expressions.

The factored form of first denominator.

b2+6b+9=(b+3)(b+3)

The factored form of second denominator.

b2-2b-15=(b-5)(b+3)

The fractions in factored form is4(b+3)(b+3),2b(b-5)(b+3).

03

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

4(b-5)(b+3)(b+3)(b-5),2b(b+3)(b-5)(b+3)(b+3)

04

Simplify the numerators.

Multiply the numerator using distributive property.

4b-20(b+3)(b+3)(b-5),2b2+6b(b+3)(b+3)(b-5).

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