Rational Expression Calculator

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.

Frequently Asked Questions

What is a rational expression?

A fraction whose numerator and denominator are polynomials, like (x²−1)/(x+1). It behaves like a numeric fraction, but the “numbers” are expressions.

How do you simplify one?

Factor the top and bottom completely, cancel factors common to both, and record which x-values the original denominator excluded.

What are domain restrictions?

Values that make the original denominator zero are excluded from the domain — even if they cancel out during simplification, the original expression was undefined there.

Is this calculator free?

Yes — every tool on Math Solver Free is free with no sign-up, and all calculations run in your browser.