   Chapter 4.1, Problem 58PS

Chapter
Section
Textbook Problem

For Problems 51-58, simplify each rational expression. You will need to use factoring by grouping. (Objective 2) n r − 6 − 3 n + 2 r n r + 10 + 2 r + 5 n

To determine

To Find:

The expression by simplifying the given rational expression.

Explanation

Approach:

A rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(n,r)q(n,r) where p(n,r) and q(n,r) are polynomials in such a way that the variables n and r do not assume values such that q(n,r)=0.

For values of n and r where q(n,r) and k(n,r) are both nonzero expressions, then by the fundamental principle of fractions, for all polynomials p(n,r), the following holds.

p(n,r)k(n,r)q(n,r)k(n,r)=p(n,r)q(n,r).

Calculation:

The given rational expression is nr63n+2rnr+10+2r+5n.

Factorise the numerator nr63n+2r.

nr63n+2r=nr3n+2r6=n(r3)+2(r3)=(n+2)(r3)

Factorise the denominator nr+10+2r+5n

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