Rational expressions are fractions with polynomials in the numerator and denominator. They look intimidating, but they follow the same rules as regular fractions.
Simplifying Rational Expressions
Factor the numerator and denominator, then cancel common factors.
Example 1: Simplify
Factor the numerator (difference of squares):
Example 2: Simplify
Multiplying Rational Expressions
Factor everything first, then cancel across numerators and denominators.
Example 3: Multiply
Dividing Rational Expressions
Flip the second fraction and multiply.
Example 4: Divide
Adding and Subtracting (Common Denominator)
Just like regular fractions, you need a common denominator.
Example 5: Add
Common denominator:
Example 6: Subtract
Common denominator:
Solving Equations with Rational Expressions
Example 7: Solve
Multiply everything by :
Use the quadratic formula:
Practice Problems
Problem 1: Simplify
Solution
Problem 2: Add
Solution
Problem 3: Simplify
Solution
Key Takeaways
- Always factor before canceling — never cancel individual terms
- Multiplying: factor everything, cancel across all numerators and denominators
- Adding/subtracting: find the LCD, combine, then simplify
- When solving equations, multiply both sides by the LCD to clear fractions
- Always note restrictions (values that make a denominator zero)
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