Chapter 4.CR, Problem 4CR

### 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 1-6, simplify each rational expression. x 4 − 1 x 3 − x

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 x4âˆ’1x3âˆ’x.

Factorise the numerator x4âˆ’1.

x4âˆ’1=(x2)2âˆ’12=(x2+1)(x2âˆ’1)=(x2+1)(x+1)(xâˆ’1)

Factorise the denominator x3âˆ’x

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