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Chapter 8: Q 177 (page 953)

Write as equivalent rational expression with LCD(x-4)(x+2)(x+3) of5x2-2x-8,2xx2-x-12.

Short Answer

Expert verified

The rational expression is5x+15(x-4)(x+2)(x+3),2x2+4x(x-4)(x+3)(x+2).

Step by step solution

01

Given Information

The given expression is5x2-2x-8,2xx2-x-12.

The LCD is(x-4)(x+2)(x+3).

02

Factor the denominator of both expressions.

The factored form of first denominator.

x2-2x-8=(x-4)(x+2)

The factored form of second denominator.

x2-x-12=(x-4)(x+3)

The fractions in factored form is5(x-4)(x+2),2x(x-4)(x+3).

03

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

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

04

Simplify the numerators.

Multiply the numerator using distributive property.

5x+15(x-4)(x+2)(x+3),2x2+4x(x-4)(x+3)(x+2).

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