   Chapter 4.CR, Problem 23CR

Chapter
Section
Textbook Problem

For Problems 11-24, perform the indicated operation and express your answers in simplest form. 8 x 2 x − 6 ÷ 2 x − 1 x 2 − 9 ⋅ 2 x 2 + x − 1 x 2 + 7 x + 12

To determine

To Perform:

The given operation and reduce it in simplest form.

Explanation

Rational expression demarcate as a 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.

If ab and cd are rational numbers, then the rational multiplication:

abcd=acbd=acbd

And the rational division:

If m and k are integers but not zero and n is any integer, then the two fractions nkmk and nm follow the fraction’s fundamental principle as given below.

nkmk=nm.

Calculation:

The given rational expression is 8x2x6÷2x1x292x2+x1x2+7x+12.

Use rational multiplication, division factorization to simplify the given expression,

8x2x6÷2x1x292x2+x1x2+7x+12=8x2x6x292x12x2+x1x2+7x+12=8x(x29)(2x2+x1)(2x6

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