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Rational Expression Calculator

Simplify, add, subtract, multiply, divide, factor and decompose rational expressions in x — e.g. (x^2-1)/(x-1) → x+1 — using exact polynomial arithmetic and partial fractions.

Related tools

All Algebra & equations tools →
Rational Equation SolverSolve rational (fraction) equations by clearing denominators to a polynomial, then excluding roots that make any denominator zero — reporting solutions, excluded values, no-solution and identity cases.Rational Root Theorem CalculatorEvery ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.Algebraic Expression SimplifierCombines like terms, expands or factors, with implicit multiplication understood (2x is 2·x). When a cancellation removes a factor, the excluded value is stated — (x²−4)/(x−2) is x+2 only for x ≠ 2, and that restriction is part of the answer.Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Absolute Value Inequality SolverSolve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.Beta Function CalculatorCompute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.Boolean Algebra SimplifierReduces a boolean expression to a minimal sum of products, accepting every common notation — AB, A·B, A&B for AND, A+B or A|B for OR, ~A, !A or A' for NOT, plus XOR, NAND and NOR. Shows the prime implicants, not just the final answer.Complementary Error Function CalculatorCompute erfc(x) = 1 − erf(x) to high precision, accurate even far in the tail.

Rational Expression Calculator is free to use as often as you like, directly from this page. You will find it under Algebra & equations, with Rational Equation Solver and Rational Root Theorem Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Rational Expression Calculator?

Simplify, add, subtract, multiply, divide, factor and decompose rational expressions in x — e.g. (x^2-1)/(x-1) → x+1 — using exact polynomial arithmetic and partial fractions.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Rational Expression Calculator different from Rational Equation Solver?

They sit next to each other but answer different questions: Rational Equation Solver is the one to open when you need it to solve rational (fraction) equations by clearing denominators to a polynomial, then excluding roots that make any denominator zero — reporting solutions, excluded values, no-solution and identity cases. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Rational Root Theorem Calculator is the closest one after this: Every ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.

What else is worth having open alongside it?

Algebraic Expression Simplifier and Absolute Value Equation Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.