1. ## Rational 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)

2. Originally Posted by magentarita
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)
Improper Rational Expression
A rational expression in which the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

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.

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

(1) Proper Rational Expression

(2) Improper Rational Expression

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

Now, perform long division to arrive at:

$2x+\frac{6x}{x^2+1}$

3. ## ok now....

Originally Posted by masters
Improper Rational Expression

A rational expression in which the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

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.

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

(1) Proper Rational Expression

(2) Improper Rational Expression

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

Now, perform long division to arrive at:

$2x+\frac{6x}{x^2+1}$
This is the exact detail that I look forward to each time I post questions.

My precalculus course is coming to an end in a few weeks.

4. Originally Posted by magentarita
This is the exact detail that I look forward to each time I post questions.

My precalculus course is coming to an end in a few weeks.
Thanks a bunch. I didn't post the details of the polynomial long division. I sort of assumed you could do that.