# Rewrite Rational Expressions (Long Division)

These lessons, with videos, examples and step-by-step solutions, help High School students learn how to rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of  b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

### Suggested Learning Targets

• Rewrite rational expressions,
a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) by using factoring, long division, or synthetic division.

• Use a computer algebra system for complicated examples to assist with building a broader conceptual understanding.

Common Core: HSA-APR.D.6

Rewriting simple rational expressions in different forms (Common Core A-APR.6)
Polynomial Division: Long Division.

Ex 1: Divide a Trinomial by a Binomial Using Long Division
This video provides two basic examples of how to divide a degree two trinomial by a degree one binomial.

Ex 2: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are no missing terms in the dividend. The quotient has a remainder.

Ex 3: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has a remainder.

Ex 4: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has no remainder.

Ex 5: Divide a Polynomial by a Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree one binomial. There are missing terms in the dividend. The quotient has fractional coefficients and there is a remainder.

Ex 6: Divide a Polynomial by a Degree Two Binomial Using Long Division
This video provides an example of how to perform long division by dividing a degree three polynomial by a degree two binomial. The quotient has a remainder.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.