Thread: 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)

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



Now, perform long division to arrive at:

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



Now, perform long division to arrive at:

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.

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.