Rational Expression Calculator

Simplify algebraic fractions and keep the original domain restrictions with the answer.

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Enter a rational expression, such as (x^2 - 9)/(x^2 - x - 6)

Try an example

Factor first, then reduce

A rational expression is a quotient of polynomials. Simplifying it means canceling common factors, not canceling separate terms across addition or subtraction.

Values that make an original denominator zero stay excluded even if their factor later cancels. For addition and subtraction, build the least common denominator before combining numerators.

How to use the rational expression calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Cancel common factors

Only a factor of the entire numerator and denominator can cancel, and its zero restriction remains.

\frac{ab}{a c} = \frac{b}{c} (a \neq = 0)

A reliable way to work through it

Record excluded values

Set every original denominator equal to zero before simplifying.

Factor the polynomials

Common factors become visible only after numerators and denominators are factored.

Use the least common denominator

For sums and differences, rewrite each fraction with a shared denominator before combining.

Worked example

Simplify (x² - 9) / (x² - x - 6)

x^{2} - 9 = (x - 3) (x + 3)

Factor the difference of squares.

x^{2} - x - 6 = (x - 3) (x + 2)

Factor the denominator.

\frac{( x - 3 ) ( x + 3 )}{( x - 3 ) ( x + 2 )} = \frac{x + 3}{x + 2}

Cancel the common factor.

The simplified form is (x + 3)/(x + 2), with x ≠ 3 and x ≠ -2.

Common mistakes to check

Canceling across addition

In (x + 3)/x, the x is not a factor of the entire numerator.

Forgetting an excluded value

A canceled denominator factor still marks a hole in the original expression.

Adding denominators

Fractions must share a denominator before their numerators can be combined.

Factoring CalculatorBreak a polynomial into factors using the pattern that fits, then verify by expanding.Simplify CalculatorCombine like terms, reduce fractions, and rewrite expressions in a cleaner equivalent form.Polynomial CalculatorWork with polynomial operations, factors, roots, and remainders in one place.Inequality CalculatorSolve an inequality, track sign changes, and write the answer in interval notation.

Questions students ask

Does the calculator list excluded values?

Yes. It checks the original denominators and keeps those restrictions even after factors cancel.

Can it solve rational equations?

Yes. It can clear denominators, solve the resulting equation, and reject answers outside the original domain.

Can it add rational expressions with different denominators?

Yes. It factors the denominators, builds a least common denominator, and combines the adjusted numerators.

Why can a canceled factor still matter?

Canceling creates an equivalent expression only where the canceled factor is nonzero. The original zero remains excluded.