   Chapter 4.4, Problem 34PS

Chapter
Section
Textbook Problem

For Problems 1-40, perform the indicated operations, and express your answers in simplest form. (Objective 1) 2 x + 5 x 2 + 3 x − 18 − 3 x − 1 x 2 + 4 x − 12 + 5 x − 2

To determine

To Find:

The simplest expression of 2x+5x2+3x183x1x2+4x12+5x2.

Explanation

Approach:

If ab and cd are rational, then addition or subtraction of rational formed by multiplying them by appropriate expressions and equating the denominators using LCD and perform the operation as below:

And,

Same algebra is used for rational expression.

Calculation:

The given expression:2x+5x2+3x183x1x2+4x12+5x2.

Factorise the terms.

2x+5x2+3x183x1x2+4x12+5x2=2x+5x2+6x3x183x1x2+6x2x12+5x2=2x+5x(x+6)3(x+6)3x1x(x+6)2(x+6)+5x2=2x+5(x3)(x+6)3x1(x2)(x+6)+5x2

The LCD of the denominator is (x2)(x+6)(x3) where x3,x2orx6

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