Chapter 11.5, Problem 6AYU

In Problems 5-12, tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. $\frac{5x+2}{x^3-1}$

To determine

To find: The given rational expression is proper or improper. If improper, to rewrite it as the sum of a polynomial and a proper rational expression.

Answer to Problem 6AYU

Solution:

The rational expression is proper.

Explanation of Solution

Given:

$\frac{5x + 2}{x^3 - 1}$.

Calculation:

By definition, a rational expression $\frac{P}{Q}$ is called proper if the degree of polynomial in the numerator is less than the degree of polynomial in the denominator.

Here the degree of the polynomial in the numerator is 1 and the degree of the polynomial is 3 in the denominator.

Therefore, the given rational expression is proper.