   Chapter 4.1, Problem 42PS

Chapter
Section
Textbook Problem

For Problems 9-50, simplify each rational expression. (Objective 2) 3 + x − 2 x 2 2 + x − x 2

To determine

To Find:

The expression by simplifying the given rational expression.

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 rational expression is 3+x2x22+xx2.

Factorise the numerator 3+x2x2.

3+x2x2=(2x2x3)=2x23x+2x3={x(2x3)+1(2x3)}={(x+1)}(2x3)

Factorise the denominator 2+xx2.

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