How to Solve Rational Expressions

A rational expression is an expression whose numerator and denominator are polynomials. For example 2x+3/4+5x is a rational expression. There are many ways of solving a rational expression, one must be able to simplify the rational expression, as well as add subtract multiply and divide to obtain an answer.

Difficulty: Moderate

Instructions

Things You'll Need:

• Paper
• Pencil
• Calculator

Simplifying Rational Expressions

1. Factor the polynomials in the numerator.

2. Factor the polynomials in the denominator.

3. Cancel out the common factors in the rational expression.

Adding and Subtracting Rational Expressions

4. Find the like denominators in the rational expressions if they do not already have like denominators. To Find like denominators find the least common factors in the denominators.

5. Add or subtract the numerators of the rational expressions with the like denomiators.

6. Simplify the rational expressions into lowest terms.

Multiply and Divide Rational Expressions

7. Factor the rational expressions.

8. Multiply the rational expressions.

9. Divide rational expressions by multiplying the first rational expression by the reciprocal of the second rational expression. Follow the steps for multiplying fractions.

Tips & Warnings

• To solve rational expressions it is important to know how to: find the least common denominator, identify polynomials, factor polynomials and add, subtract, multiply and divide fractions.

Resources

• Examples of Rational Expressions and Problems

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