Rational Expressions Calculator
Simplify, add, subtract, multiply, and divide rational expressions with step-by-step solutions
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Fraction 1
Theory & Formula
Rational Expressions
Rational expressions are fractions where both the numerator and denominator are polynomials. Operations on rational expressions follow similar rules to arithmetic with fractions.
Operations
Addition
\(\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\)
Subtraction
\(\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}\)
Multiplication
\(\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\)
Division
\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\)
Simplification
To simplify a rational expression, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.
Example: \(\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}\)
Restrictions
- The denominator cannot be zero
- Always identify values that would make the denominator zero (excluded values)