   Chapter 4.4, Problem 27PS

Chapter
Section
Textbook Problem

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

To determine

To Find:

The simplest expression of xx2x2+3x24.

Explanation

Approach:

The rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(x)q(x), where p(x) and q(x) are polynomials, while for any values of x the denominator q(x)0.

For values of x, where q(x) and k(x) are both nonzero expressions, then for all polynomials p(x), the following holds.

p(x)k(x)q(x)k(x)=p(x)q(x).

Calculation:

The given expression is xx2x2+3x24.

Factorise the terms.

xx2x2+3x24=xx2x2+3x2(2)2=xx2x2+3(x2)(x+2)

The LCD of the denominator is (x2)(x+2) where x2orx2

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