Algebra
Rational expressions
Polynomials in fractions. Add, subtract, multiply, divide — same rules as fractions.
A rational expression is a fraction whose top and bottom are polynomials. Treat them like number fractions — same rules.
Walk through
Step 1 of 4
The expression
Simplify (x² − 4)/(x + 2).
Same rules as number fractions
- Simplify: factor everything, cancel common factors (not terms).
- Multiply: multiply numerators and denominators, then cancel.
- Divide: multiply by the reciprocal of the second fraction.
- Add/subtract: get a common denominator first.
Your turn
Simplify (x² + 3x)/(x² − 9).
Watch out
You can cancel factors, not pieces of a sum. (x + 2)/x is not 2 — the x on top is added, not multiplied, so nothing cancels.
Try it
Simplify (x² − 4)/(x + 2)
Factor top: (x−2)(x+2). Cancel (x+2): x − 2.