Q. 6 - 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 

$6. \frac{5x+2}{x^3-1}$

Step-by-Step Solution

Answer

The given rational expression is proper 

Step 1. Given data

The given expression is $\frac{5x+2}{x^3-1}$.

Step 2. Find the expression is proper or improper

We have the given expression$\frac{5x+2}{x^3-1}$

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

The degree of the polynomial in the denominator $=3$

Here the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator.

Hence, the given rational expression is proper.