Chapter 4.CR, Problem 23CR

### 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 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:

abâ‹…cd=aâ‹…cbâ‹…d=acbd

And the rational division:

If m and k are integers but not zero and n is any integer, then the two fractions nâ‹…kmâ‹…k and nm follow the fractionâ€™s fundamental principle as given below.

nâ‹…kmâ‹…k=nm.

Calculation:

The given rational expression is 8x2xâˆ’6Ã·2xâˆ’1x2âˆ’9â‹…2x2+xâˆ’1x2+7x+12.

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

8x2xâˆ’6Ã·2xâˆ’1x2âˆ’9â‹…2x2+xâˆ’1x2+7x+12=8x2xâˆ’6â‹…x2âˆ’92xâˆ’1â‹…2x2+xâˆ’1x2+7x+12=8x(x2âˆ’9)(2x2+xâˆ’1)(2xâˆ’6

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