Chapter 4.2, Problem 42PS

### 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) t 4 − 81 t 2 − 6 t + 9 ⋅ 6 t 2 − 11 t − 21 5 t 2 + 8 t − 21

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 is t4âˆ’81t2âˆ’6t+9â‹…6t2âˆ’11tâˆ’215t2+8tâˆ’21.

Use rational multiplication and factorization to simplify the given expression.

t4âˆ’81t2âˆ’6t+9â‹…6t2âˆ’11tâˆ’215t2+8tâˆ’21=(t4âˆ’81)(6t2âˆ’11tâˆ’21)(t2âˆ’6t+9)(5t2+8tâˆ’21)={(t2)2âˆ’92}(6t2âˆ’18t+7tâˆ’21)(t2âˆ’3tâˆ’3t+9)(5t2+15tâˆ’7tâˆ’21)=<

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