   Chapter 4.1, Problem 67PS

Chapter
Section
Textbook Problem

For Problems 59-68, simplify each rational expression. You may want to refer to Example 12 of this section. (Objective 2) n 2 − 5 n − 24 40 + 3 n − n 2

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)q(n) where p(n) and q(n) are polynomials in such a way that the variable n does not assume values such that q(n)=0.

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

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

Calculation:

The given rational expression is n25n2440+3nn2.

Factorise the numerator n25n24.

n25n24=n28n+3n24=n(n8)+3(n8)=(n+3)(n8)

Factorise the denominator 40+3nn2.

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