Chapter 4.2, Problem 40PS

### 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) 21 t 2 + t − 2 2 t 2 − 17 t − 9 ÷ 12 t 2 − 5 t − 3 8 t 2 − 2 t − 3

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 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 21t2+tâˆ’22t2âˆ’17tâˆ’9Ã·12t2âˆ’5tâˆ’38t2âˆ’2tâˆ’3.

Use rational division and factorization to simplify the given expression,

21t2+tâˆ’22t2âˆ’17tâˆ’9Ã·12t2âˆ’5tâˆ’38t2âˆ’2tâˆ’3=(21t2+tâˆ’2)(8t2âˆ’2tâˆ’3)(2t2âˆ’17tâˆ’9)(12t2âˆ’5tâˆ’3)=(21t2+7tâˆ’6tâˆ’2)(8t2âˆ’6t+4tâˆ’3)(2t2âˆ’18t+tâˆ’9)(12t2âˆ’9t+4t<

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