Chapter 11.5, Problem 5AYU

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. $\frac{x}{x^2-1}$

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 5AYU

Solution:

The rational expression is proper.

Explanation of Solution

Given:

$\frac{x}{x^2 - 1}$

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 2 in the denominator.

Therefore, the given rational expression is proper.