Rational Expressions
Simplify, multiply, divide, add, and subtract rational expressions
lessons (10)
Introduction to Rational Expressions
Learn what rational expressions are, how to identify them, and understand their key properties including domain restrictions.
Simplifying Rational Expressions
Learn how to reduce rational expressions to their simplest form by factoring and canceling common factors.
Multiplying Rational Expressions
Learn to multiply rational expressions by multiplying numerators and denominators, then simplifying.
Dividing Rational Expressions
Learn how to divide rational expressions by multiplying by the reciprocal.
Adding Rational Expressions (Like Denominators)
Learn how to add rational expressions that share the same denominator by combining numerators.
Subtracting Rational Expressions (Like Denominators)
Learn how to subtract rational expressions that share the same denominator by combining numerators.
Finding the LCD of Rational Expressions
Learn how to find the least common denominator (LCD) of rational expressions to add and subtract them.
Adding Rational Expressions (Unlike Denominators)
Learn how to add rational expressions with different denominators by finding the LCD.
Complex Fractions
Learn how to simplify fractions that contain fractions in the numerator, denominator, or both.
Solving Rational Equations
Learn how to solve equations containing rational expressions by finding the LCD and eliminating denominators.
Rational expressions are fractions with polynomials in the numerator and denominator. They appear throughout advanced mathematics, physics, and engineering whenever rates, proportions, or inverse relationships are involved. Mastering rational expressions builds on your fraction skills while preparing you for calculus concepts like limits and asymptotes.
In this topic, you will simplify rational expressions by factoring and canceling common factors. You will add, subtract, multiply, and divide these algebraic fractions, finding common denominators when needed. Understanding restrictions on variables and domain is crucial for working correctly with these expressions.
Our lessons connect rational expressions to practical applications like work rate problems, mixture problems, and electrical circuits. You will solve rational equations and learn to check for extraneous solutions. These skills are essential for pre-calculus and beyond.
What Students Will Learn
- Simplify rational expressions by factoring
- Find the domain of rational expressions
- Multiply and divide rational expressions
- Add and subtract rational expressions with unlike denominators
- Simplify complex fractions
- Solve rational equations
- Identify and check for extraneous solutions
Frequently Asked Questions
What makes a value excluded from the domain?
Any value that makes the denominator zero is excluded from the domain because division by zero is undefined. Always factor the denominator and set each factor equal to zero to find restrictions.
What is an extraneous solution?
An extraneous solution is a value that satisfies the transformed equation but not the original. It typically comes from excluded domain values. Always check solutions in the original equation.
How do I find a common denominator for rational expressions?
Factor each denominator completely. The LCD includes each factor the maximum number of times it appears in any single denominator. Then convert each fraction to have this LCD.