Chapter 4.2, Problem 39PS

### 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 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. (Objective 2, 4 and 5) 3 x 2 − 20 x + 25 2 x 2 − 7 x − 15 ÷ 9 x 2 − 3 x − 20 12 x 2 + 28 x + 15

To determine

To perform:

The given operation and reduce it in simplest form.

Explanation

Approach:

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: 3x2âˆ’20x+252x2âˆ’7xâˆ’15Ã·9x2âˆ’3xâˆ’2012x2+28x+15.

Use rational division and factorization to simplify the given expression,

3x2âˆ’20x+252x2âˆ’7xâˆ’15Ã·9x2âˆ’3xâˆ’2012x2+28x+15=3x2âˆ’20x+252x2âˆ’7xâˆ’15â‹…12x2+28x+159x2âˆ’3xâˆ’20=(3x2âˆ’15xâˆ’5x+25)(12x2+10x+18x+15)

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