Rational Expression Calculator
Simplify, add, subtract, multiply, and divide rational expressions with step-by-step solutions
Understanding Rational Expressions
A rational expression is a fraction where both the numerator and denominator are polynomials. Just like numerical fractions, we can perform operations on rational expressions including simplification, addition, subtraction, multiplication, and division.
Key Concepts
- Restrictions: Values that make the denominator zero
- Simplification: Cancel common factors in numerator and denominator
- LCD: Least Common Denominator needed for addition/subtraction
- Cross-cancellation: Simplify before multiplying
- Keep-Change-Flip: Division becomes multiplication by reciprocal
Frequently Asked Questions
What is a rational expression?
A rational expression is a fraction where both the numerator and denominator are polynomials. Examples include (x+2)/(x-3) or (x²-4)/(x²-1).
Why do we need to find restrictions?
Restrictions identify values that would make the denominator zero, which would make the expression undefined. These values must be excluded from the domain.
How do you simplify a rational expression?
Factor both numerator and denominator completely, then cancel any common factors. Remember to state restrictions based on the original denominator.
What's the difference between simplifying before vs after operations?
It's often easier to factor and cancel before performing operations (especially multiplication) to work with simpler expressions.
How do you add or subtract rational expressions?
Find the least common denominator (LCD), convert each fraction to have this denominator, then add or subtract the numerators. Finally, simplify if possible.
What is the Keep-Change-Flip rule?
When dividing rational expressions, keep the first fraction, change division to multiplication, and flip (take the reciprocal of) the second fraction.
Can rational expressions have multiple restrictions?
Yes! Any value that makes any denominator (original or after operations) equal to zero is a restriction.
What if the numerator and denominator have no common factors?
If there are no common factors after factoring, the rational expression is already in simplest form. You still need to state the restrictions.