   Chapter 4.2, Problem 45PS

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) n r + 3 n + 2 r + 6 n r + 3 n − 3 r − 9 ⋅ n 2 − 9 n 3 − 4 n

To determine

To perform:

The given operation and reduce it in simplest form.

Explanation

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 nr+3n+2r+6nr+3n3r9n29n34n.

Use rational multiplication and factorization to simplify the given expression.

nr+3n+2r+6nr+3n3r9n29n34n=(nr+3n+2r+6)(n29)(nr+3n3r9)(n34n)=(nr+3n+2r+6)(n29)(nr<

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