   Chapter 4.3, Problem 67PS

Chapter
Section
Textbook Problem

Recall that the indicated quotient of a polynomial and its opposite is − 1 . For example, x − 2 2 − x simplifies to − 1 . Keep this idea in mind as you add or subtract the following rational expressions.(a) 1 x − 1 − x x − 1 (b) 3 2 x − 3 − 2 x 2 x − 3 (c) 4 x − 4 − x x − 4 + 1 (d) − 1 + 2 x − 2 − x x − 2

To determine

(a).

To solve:

The operation 1x1xx1.

Explanation

Approach:

A 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 in such a way that the variable x does not assume values such that q(x)=0.

For values of x where q(x) and k(x) are both nonzero expressions, then by the fundamental principle of fractions, 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 1x1xx1

To determine

(b).

To solve:

The operation 32x32x2x3.

To determine

(c).

To solve:

The operation 4x4xx4+1.

To determine

(d).

To solve:

The operation 1+2x2xx2.

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