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.

How do I perform the indicated operation and simplify rational expressions?

Type the whole operation, with parentheses around any numerator or denominator that has more than one term, then choose Simplify expression. For example, x/(x + 1) + 1/(x - 1) becomes (x^2 + 1)/(x^2 - 1), with x ≠ -1 and x ≠ 1 kept from the original denominators. Subtraction, multiplication and division work the same way. When a common factor cancels, the steps name it: (x^2 - 9)/(x^2 + 5x + 6) becomes (x - 3)/(x + 2) after dividing by x + 3.

Can it simplify a complex fraction?

Yes. Type the fraction inside a fraction with parentheses around the top and bottom. (1/x + 1)/(1/x - 1) becomes (-x - 1)/(x - 1), and the domain keeps x ≠ 0 from the inner fractions and x ≠ 1 from the outer denominator. Numeric complex fractions work too: (1/2)/(3/4) is 2/3.

Does it follow the order of operations with fractions?

Yes. Powers come first, then multiplication and division, then addition and subtraction, with parentheses overriding all of them. So 1/2 + 3/4 * 2/3 is 1/2 + 1/2 = 1, while (1/2 + 3/4) * 2/3 is 5/6. Every fraction stays exact, with no decimal rounding.

Can it simplify a rational function?

Type the function's formula without the f(x) = part. The result is the reduced formula, and the domain lists every condition the original denominators impose. When an excluded value no longer makes the reduced denominator zero, the original graph has a hole there: (x^2 - 1)/(x - 1) reduces to x + 1, and checking x = 1 shows the reduced formula alone gives 2, so the hole is at (1, 2).

Can it simplify an equation?

Yes. Type one equals sign and each side is simplified separately, with both sides' excluded values kept: 3(x + 2) - x = (x^2 - 9)/(x - 3) becomes 2x + 6 = x + 3 with x ≠ 3. Nothing moves across the equals sign and the equation is not solved.

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 -20 to 20. Put a negative power in parentheses, x^(-2), or type x⁻²; the result is written with positive exponents. 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 and fractional 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, and a negative power such as x^(-3) becomes 1/x^3 with the same condition. 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.

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.

ExpressionExact rational algebra

Your expression

17 / 2,000 charactersCtrl or ⌘ + Enter to run

Up to 3 real variables, integer powers -20 to 20 and one optional equals sign. 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.

Put a negative power in parentheses, x^(-2), or type x⁻²; the result is written with positive exponents. Zero and negative powers require a nonzero base: x^0 = 1 only where x ≠ 0.

One equals sign, as in 2(x + 1) = x/x, simplifies each side separately. The equation is not solved. Functions, radicals, scientific notation and variable or fractional exponents are unsupported.

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)

Value of x

Exact values agree

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.

Simplified expressionExample preview

Original domain

x ≠ 1

These conditions remain after cancellation.

Inspect original divisors and zero- or negative-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 or negative 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

Result terms2

Variables1

Domain conditions1

ArithmeticExact rational

Complete text and LaTeX output

Complete expression and domain

x + 1
Domain: x ≠ 1

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, integer powers from -20 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions and radicals are unsupported, and an equation's two sides are simplified separately, not solved. 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.
How do I perform the indicated operation and simplify rational expressions?: Type the whole operation, with parentheses around any numerator or denominator that has more than one term, then choose Simplify expression. For example, x/(x + 1) + 1/(x - 1) becomes (x^2 + 1)/(x^2 - 1), with x ≠ -1 and x ≠ 1 kept from the original denominators. Subtraction, multiplication and division work the same way. When a common factor cancels, the steps name it: (x^2 - 9)/(x^2 + 5x + 6) becomes (x - 3)/(x + 2) after dividing by x + 3.
Can it simplify a complex fraction?: Yes. Type the fraction inside a fraction with parentheses around the top and bottom. (1/x + 1)/(1/x - 1) becomes (-x - 1)/(x - 1), and the domain keeps x ≠ 0 from the inner fractions and x ≠ 1 from the outer denominator. Numeric complex fractions work too: (1/2)/(3/4) is 2/3.
Does it follow the order of operations with fractions?: Yes. Powers come first, then multiplication and division, then addition and subtraction, with parentheses overriding all of them. So 1/2 + 3/4 * 2/3 is 1/2 + 1/2 = 1, while (1/2 + 3/4) * 2/3 is 5/6. Every fraction stays exact, with no decimal rounding.
Can it simplify a rational function?: Type the function's formula without the f(x) = part. The result is the reduced formula, and the domain lists every condition the original denominators impose. When an excluded value no longer makes the reduced denominator zero, the original graph has a hole there: (x^2 - 1)/(x - 1) reduces to x + 1, and checking x = 1 shows the reduced formula alone gives 2, so the hole is at (1, 2).
Can it simplify an equation?: Yes. Type one equals sign and each side is simplified separately, with both sides' excluded values kept: 3(x + 2) - x = (x^2 - 9)/(x - 3) becomes 2x + 6 = x + 3 with x ≠ 3. Nothing moves across the equals sign and the equation is not solved.
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 -20 to 20. Put a negative power in parentheses, x^(-2), or type x⁻²; the result is written with positive exponents. 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 and fractional 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, and a negative power such as x^(-3) becomes 1/x^3 with the same condition. 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, integer powers from -20 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions and radicals are unsupported, and an equation's two sides are simplified separately, not solved. A result is a canonical rational form, not a claim of the shortest possible expression.