Chapter 4.1, Problem 42PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
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)â‹…k(x)q(x)â‹…k(x)=p(x)q(x).

Calculation:

The given rational expression is 3+xâˆ’2x22+xâˆ’x2.

Factorise the numerator 3+xâˆ’2x2.

3+xâˆ’2x2=âˆ’(2x2âˆ’xâˆ’3)=âˆ’2x2âˆ’3x+2xâˆ’3=âˆ’{x(2xâˆ’3)+1(2xâˆ’3)}={âˆ’(x+1)}(2xâˆ’3)

Factorise the denominator 2+xâˆ’x2.

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