Math Solver

Cancel factors, keep the domain

Rational Expression Calculator

Simplify polynomial fractions or solve a bounded rational equation without losing the values excluded by the original denominators. Both the algebra and the real domain are checked independently.

Simplify a rational expressionSee the boundary
Status
Verified
Maximum degree
2
Domain
Real numbers
Independent check
Identity + domain

The domain is part of the answer

Common factors may cancel algebraically, but an input that made the original expression undefined cannot be restored. Math Solver therefore displays the simplified fraction together with every preserved denominator restriction.

Cancel a common factor

x2−1x−1=x+1,x≠1\frac{x^2-1}{x-1}=x+1,\quad x\ne1

Combine two fractions

1x−1+1x+1=2xx2−1\frac{1}{x-1}+\frac{1}{x+1}=\frac{2x}{x^2-1}

Solve and filter

x+1x−2=3⇒x=72\frac{x+1}{x-2}=3\Rightarrow x=\frac{7}{2}

Current limitations

  • One variable and exact rational coefficients only.
  • Numerators, denominators, and intermediate products must remain degree two or lower.
  • Rational inequalities, variable radicals, and multivariable forms are not supported.
  • Unsupported forms fail closed instead of silently dropping domain conditions.

Questions

Rational expression calculator FAQ

Why does the answer keep an excluded value after cancellation?

Cancelling a common factor changes the written form, not the original domain. A value that made an original denominator zero remains excluded from the simplified result.

How are rational equations checked?

The solver reduces the equation to an exact numerator equation, solves it, removes candidates forbidden by any original denominator, and independently compares the complete real solution set.

Which rational forms are supported?

The current boundary is one variable with exact rational coefficients, with numerators, denominators, and intermediate products staying at degree two or lower. Rational inequalities are not included.