Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

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 

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

Step-by-Step Solution

Answer

The given rational expression is proper.

Step 1. Given data

The given expression is$\frac{x}{x^2-1}$.

Step 2. Proper or improper

The rational expression $\frac{P}{Q}$is proper if the degree of the numerator is less than the degree of the denominator, otherwise, it is improper.

The degree of the polynomial in the numerator$=1$

The degree of the polynomial in the denominator $=2$

Here, in the given rational expression, $\frac{x}{x^2-1}$we can see that the degree of the numerator is less than the degree of the denominator.

Hence, the given rational expression is proper.