   Chapter 4.2, Problem 42PS

Chapter
Section
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:

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 t481t26t+96t211t215t2+8t21.

Use rational multiplication and factorization to simplify the given expression.

t481t26t+96t211t215t2+8t21=(t481)(6t211t21)(t26t+9)(5t2+8t21)={(t2)292}(6t218t+7t21)(t23t3t+9)(5t2+15t7t21)=<

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