   Chapter 4.CR, Problem 4CR

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

Calculation:

The given rational expression is x41x3x.

Factorise the numerator x41.

x41=(x2)212=(x2+1)(x21)=(x2+1)(x+1)(x1)

Factorise the denominator x3x

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