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Chapter 8: Q 179 (page 953)

Write as equivalent rational expression with LCD(z-2)(z+4)(z+2)of9z2+2z-8,4zz2-4.

Short Answer

Expert verified

The result is9z+18(z+4)(z-2)(z+2),4z2+16z(z+2)(z-2)(z+4)

Step by step solution

01

Given Information

The given expression is9z2+2z-8,4zz2-4.

The LCD is(z-2)(z+4)(z+2).

02

Factor the denominator of both expressions.

The factored form of first denominator.

z2+2z-8=(z+4)(z-2)

The factored form of second denominator.

z2-4=(z+2)(z-2)

The fractions in factored form is9(z+4)(z-2),4z(z+2)(z-2).

03

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

9(z+2)(z+4)(z-2)(z+2),4z(z+4)(z+2)(z-2)(z+4)

04

Simplify the numerators.

Multiply the numerator using distributive property.

9z+18(z+4)(z-2)(z+2),4z2+16z(z+2)(z-2)(z+4).

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