# Rational Expressions and Equations

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More Lessons for Algebra

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A series of free, online Basic Algebra Lessons.

In this lesson, we will learn

• how to multiply and divide rational expressions
• how to add and subtract rational expressions
• how to solve rational equations

Multiplying and Dividing Rational Expressions
Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.

This video explains how to multiply and divide rational expressions.
This video provides examples on how to multiply rational expressions when the numerators and denominators are monomials.

This video provides examples on how to multiply rational expressions.
This video provides examples on how to divide rational expressions.

Adding and Subtracting Rational Expressions
Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.

This video explains how to add and subtract rational expression with and without like denominators.
This video provides two examples of how to add and subtraction rational expressions with the the same denominators.

This video provides two examples of how to add and subtraction rational expressions when the denominators are different.
This video provides two examples of how to add and subtraction rational expressions when the denominators are different.

Solving Rational Equations
Solving rational equations is substantially easier with like denominators. When solving rational equations, first multiply every term in the equation by the common denominator so the equation is "cleared" of fractions.

When solving rational equations with unlike denominators, the first step is to factor the denominators and look for a common denominator. Next, we multiply both sides of the equation by the common denominator to clear the fractions. Finally, we solve for the variable using an appropriate technique.

This video explains how to solve rational equations.
Solving a Basic Rational Equation - Ex 1

Solving a Basic Rational Equation - Ex 2
Solving a Basic Rational Equation - Ex 3

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