How to Simplify Rational Expressions
A rational expression is a fraction of polynomials, and simplifying one works exactly like reducing 6/8 to 3/4: factor everything, then cancel what the top and bottom share.
Factor, Then Cancel
You cannot cancel terms — only factors. In (x²−1)/(x+1), the top factors to (x+1)(x−1), so the (x+1) factor cancels and you are left with x−1. Cancelling the x’s in (x+5)/x would be wrong because x is a term, not a factor.
Never Forget the Domain
Cancelling (x+1) does not erase the fact that x = −1 made the original denominator zero. Always state excluded values from the original denominator — this tool lists them automatically.
Need the factoring step explained? See our factoring calculator or practice with plain numeric fractions on the fraction calculator.