   Chapter 4.1, Problem 31PS

Chapter
Section
Textbook Problem

For Problems 9-50, simplify each rational expression. (Objective 2) 3 x 2 − 12 x x 3 − 64

To determine

To Find:

The expression by simplifying the given rational expression.

Explanation

Concept:

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 3x212xx364.

Factorise the numerator 3x212x.

3x212x=3x(x4)

Factorise the denominator x364.

x364=x343=(x4)(x2+4x+16)

Write the given fraction as,

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