   Chapter 4.2, Problem 40PS

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) 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 nkmk and nm follow the fraction’s fundamental principle as given below.

nkmk=nm.

Calculation:

The given rational expression is 21t2+t22t217t9÷12t25t38t22t3.

Use rational division and factorization to simplify the given expression,

21t2+t22t217t9÷12t25t38t22t3=(21t2+t2)(8t22t3)(2t217t9)(12t25t3)=(21t2+7t6t2)(8t26t+4t3)(2t218t+t9)(12t29t+4t<

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