Chapter 4.1, Problem 40PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For Problems 9-50, simplify each rational expression. (Objective 2) 5 n 2 + 18 n − 8 3 n 2 + 13 n + 4

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

p(n)â‹…k(n)q(n)â‹…k(n)=p(n)q(n).

Calculation:

The given rational expression is 5n2+18nâˆ’83n2+13n+4.

Factorise the numerator 5n2+18nâˆ’8.

5n2+18nâˆ’8=5n2+20nâˆ’2nâˆ’8=5n(n+4)âˆ’2(n+4)=(5nâˆ’2)(n+4)

Factorise the denominator 3n2+13n+4

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