Determine whether the given expressions are proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression.

(1) (5x + 2)/(x^3 - 1)

(2) 2x(x^2 + 4)/(x^2 + 1)

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- Oct 22nd 2008, 04:41 AMmagentaritaRational Expression
Determine whether the given expressions are proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression.

(1) (5x + 2)/(x^3 - 1)

(2) 2x(x^2 + 4)/(x^2 + 1) - Oct 23rd 2008, 07:50 AMmastersA rational expression in which the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.
**Improper Rational Expression**

Note: Polynomial long division can be used to write an improper rational expression as the sum of a polynomial and a proper rational expression. Synthetic division may also be used for some fractions.

A rational expression in which the degree of the numerator polynomial is less than the degree of the denominator polynomial.**Proper Rational Expression**

(1) Proper Rational Expression

(2) Improper Rational Expression

$\displaystyle \frac{2x(x^2+4)}{x^2+1}=\frac{2x^3+8x}{x^2+1}$

Now, perform long division to arrive at:

$\displaystyle 2x+\frac{6x}{x^2+1}$ - Oct 23rd 2008, 12:12 PMmagentaritaok now....
- Oct 23rd 2008, 12:15 PMmasters