   Chapter 4.1, Problem 50PS

Chapter
Section
Textbook Problem

For Problems 9-50, simplify each rational expression. (Objective 2) − 6 x 3 − 21 x 2 + 12 x − 18 x 3 − 42 x 2 + 120 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 6x321x2+12x18x342x2+120x.

Factorise the numerator 6x321x2+12x.

6x321x2+12x=3x(2x2+7x4)=3x(2x2+8xx4)=3x{2x(x+4)1(x+4)}=3x(2x1)(x+4)

Factorise the denominator 18x342x2+120x.

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