Simplify an Equation
Type an equation with one equals sign and each side is simplified on its own: like terms collected, products expanded and common factors cancelled. The page opens on 2(x - 4) + 3x = (x^2 - 4)/(x + 2) + 6, which becomes 5x - 8 = x + 4 with x ≠ -2 kept from the original right side. Nothing moves across the equals sign, so the equation is tidied, not solved.
37 / 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)
- Original sides
- left -3; right 5
- Simplified sides
- left -3; right 5
Each simplified side has the same exact value as the original side at this permitted substitution. A single substitution is a check, not a proof of equivalence.
At these values the two sides are not equal, so these values do not satisfy the equation.
- x ≠ -2
These conditions remain after cancellation.
Inspect original divisors and zero- or negative-power bases
(x + 2) ≠ 0- Read the equation
Use exact rational coefficients and real variables x. Adjacent letters multiply; multiplication and division are evaluated left to right.
- Keep the two sides apart
Simplify each side of the equals sign on its own. No term moves across the equals sign, and the equation is not solved.
- Preserve the original domain
Keep x ≠ -2 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.
5x - 8 = (x^2 + 6x + 8)/(x + 2) - Cancel a verified common factor
Divide the numerator and denominator of the right side by x + 2, keeping every original domain exclusion.
5x - 8 = x + 4
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, 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
- Does this solve the equation?
- No. It simplifies each side and stops, so you can see the equation in its cleanest form before solving it. From 5x - 8 = x + 4, subtracting x and adding 8 on both sides gives 4x = 12, so x = 3, which is allowed because only x = -2 is excluded.
- Why keep x ≠ -2 after the fraction cancels?
- The original right side divides by x + 2, so x = -2 makes the original equation undefined. The reduced side x + 4 hides that, which is how extraneous solutions appear. A value the domain excludes can never be a solution, even when the simplified equation accepts it.
- Can I simplify a rational equation?
- Yes. Each side is reduced to one fraction with exact coefficients, and every denominator from either side is listed in the domain. For example, x/(x - 1) = 1/(x - 1) + 1 becomes x/(x - 1) = x/(x - 1) with x ≠ 1: the sides agree everywhere except x = 1, where the original equation is undefined.
- How does the substitution check work for an equation?
- Enter a value for each variable and choose Check values. The tool compares each original side with its simplified side at that value. The page opens with x = 1, where the left side is -3 both before and after simplifying and the right side is 5 both times. The two sides differing from each other only means x = 1 is not a solution.
- What can each side contain?
- The same syntax as a single expression: +, -, *, /, parentheses, exact fractions and decimals, and integer powers from -20 to 20, with up to three variables across both sides. Use exactly one equals sign; inequalities, functions and radicals are unsupported.
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.