Expression Simplifier
Simplify rational expressions or expand products with exact fractional coefficients. See the transformation trail, keep original denominator restrictions in view, and compare both expressions at values you choose.
17 / 2,000 charactersCtrl or ⌘ + Enter to run
Up to 3 real variables, integer powers 0 to 20. Expand distributes products; Simplify also cancels shared polynomial factors.
Supported syntax and limits
Use +, -, *, /, parentheses and powers such as x^2 or x². Integers, fractions and finite decimals are exact.
2xy means 2*x*y. For a longer name, use brackets: 2[rate] + [cost]. Names have up to 24 characters and start with a letter.
Multiplication and division run left to right: 1/2x means (1/2)*x. Use 1/(2x) for a denominator of 2x.
Functions, radicals, equations, scientific notation and negative or variable exponents are unsupported. Zero powers require a nonzero base: x^0 = 1 only where x ≠ 0.
Expansion is bounded to 2,000 terms and 1,000 digits in each exact coefficient numerator or denominator. An arithmetic budget, 80 nesting levels and a 10-second worker limit prevent unbounded work. Cancel or press Escape to keep your input.
Check a substitution (optional)
- Original expression
- 4
- Result expression
- 4
The exact rational values agree at this permitted substitution. A single substitution is a check, not a proof of equivalence.
- x ≠ 1
These conditions remain after cancellation.
Inspect original divisors and zero-power bases
(x - 1) ≠ 0- Read the expression
Use exact rational coefficients and real variables x. Adjacent letters multiply; multiplication and division are evaluated left to right.
- Preserve the original domain
Keep x ≠ 1 before cancelling any factors. A zero power also requires a nonzero base.
- Distribute and collect
Expand finite integer powers and distributive products. Add coefficients only when every variable has the same power.
(x^2 - 1)/(x - 1) - Cancel a verified common factor
Divide numerator and denominator by x - 1, keeping every original domain exclusion.
x + 1
Complete text and LaTeX output
Both formats retain the original domain conditions. Select this text to copy manually.
Example preview. Edit the expression or run it to make your own result.
Try a worked example
Accuracy. Exact rational-expression algebra within 2,000 input characters, three real variables, powers from 0 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions, radicals and equations are unsupported. A result is a canonical rational form, not a claim of the shortest possible expression.
Common questions
- How do I simplify an algebraic expression?
- Enter an expression and choose Simplify expression. For example, 2x + 3x - 4 becomes 5x - 4, and 2(x + 3) - x becomes x + 6. The result includes a transformation explanation and any conditions needed for the original expression to be defined.
- What is the difference between Simplify and Expand?
- Both modes distribute products and collect like terms using exact rational coefficients. Simplify also cancels common polynomial factors from the numerator and denominator. Expand leaves those polynomial factors uncancelled in the expanded fraction. Neither mode promises the shortest possible form.
- Why does x not equal 1 remain after cancelling x minus 1?
- The original expression (x^2 - 1)/(x - 1) divides by zero at x = 1. Its simplified formula is x + 1, but that formula only represents the original expression where x is not 1. The tool retains this restriction, includes it when copying the result or LaTeX, and marks a substitution of 1 as undefined.
- Which variables and notation can I use?
- Use up to three real variables with +, -, *, /, parentheses and literal integer powers from 0 to 20. Adjacent single letters multiply: 2xy means 2*x*y. Put longer variable names in brackets, such as [rate] or [cost_1]. Names start with a letter and contain up to 24 letters, digits or underscores. Multiplication and division run left to right, so write 1/(2x) when the whole product is the denominator.
- Are decimals and fractions exact?
- Yes. Integers, finite decimals and rational fractions are processed with exact integer arithmetic, so 0.1 + 0.2 returns 3/10. Substitution values can also be signed integers, finite decimals or fractions with nonzero denominators. Scientific notation, radicals, functions, equations and noninteger or variable exponents are unsupported.
- How does the substitution check work?
- After generating a result, enter a value for every variable and choose Check values. The tool evaluates the original expression and result exactly, while checking the retained domain conditions. Agreement at a single substitution is a useful check, not a proof that arbitrary expressions are equivalent.
- What happens to zero powers and 0^0?
- This tool treats 0^0 as undefined. It simplifies x^0 to 1 with the condition x is not 0. It also keeps restrictions inside a base or a product, so (1/x)^0 and 0*(1/x) still require x not to be 0.
- What are the limits, and can I cancel a calculation?
- Input is limited to 2,000 characters, expansion to 2,000 terms, and each coefficient numerator or denominator to 1,000 digits. Combined polynomial degrees must stay within the exact integer range. There is also an arithmetic operation budget, an 80-level nesting limit and a 10-second worker limit. Exceeding a limit gives an explicit unresolved message without truncating your input. Cancel or press Escape during a calculation to stop its worker and keep the expression and substitution values.
Exact rational-expression algebra within 2,000 input characters, three real variables, powers from 0 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions, radicals and equations are unsupported. A result is a canonical rational form, not a claim of the shortest possible expression.