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: