Simplify Calculator
Type an algebraic expression to simplify it — combining like terms and cancelling common factors.
Use ^ for powers, * or implied for multiply, / for divide.
To simplify an algebraic expression, combine like terms, apply the order of operations, expand products where useful, and cancel common factors in fractions. The simplest form is an equivalent expression written as compactly as possible, such as (x² − 1)/(x − 1) simplifying to x + 1.
How to Use This Calculator
Type your expression using standard notation: ^ for exponents, / for division, and parentheses for grouping. Multiplication can be written with * or implied, so 5x and 5*x both work. The calculator returns an equivalent expression in simplest form.
Simplifying means rewriting an expression as compactly as possible without changing its value — combining like terms, expanding where it helps, and cancelling common factors in fractions.
How the Calculation Works
The calculator parses your expression into its algebraic structure and applies the standard simplification rules: like terms are added together, powers are combined, and any factor common to the numerator and denominator of a fraction is cancelled.
The result is mathematically equivalent to what you entered — it has the same value for every input — just written in a shorter, cleaner form.
combine like terms · expand products · cancel common factors
Worked Example
Take (x² − 1)/(x − 1). The numerator factors as (x − 1)(x + 1), and the (x − 1) cancels with the denominator, leaving x + 1.
Similarly, 2x + 3x simplifies to 5x by combining like terms, and 3(x + 2) expands and simplifies to 3x + 6.
Assumptions and Limitations
- Handles polynomial and rational expressions in one or more variables
- The result is equivalent but may be ordered differently from what you expect
- Cancelling (x − 1) assumes x ≠ 1, the value that would make the original undefined
- Very unusual functions may not simplify further
When to Use a Simplify Calculator
Algebra students use this to reduce an expression to its simplest form, combining like terms and clearing what can be cancelled. Run it to check homework or to see how a messy expression tidies up. Enter the expression and get the simplified result.
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Open calculator →Frequently Asked Questions
What does it mean to simplify an expression?
It means rewriting it in the most compact equivalent form — combining like terms, expanding where useful, and cancelling common factors — without changing its value for any input.
How do I enter powers and multiplication?
Use ^ for powers (x^2 for x squared) and either * or implied multiplication (5x or 5*x). Use parentheses to group, and / for division.
Why does cancelling change the domain?
Cancelling (x − 1) from (x² − 1)/(x − 1) gives x + 1, but the original was undefined at x = 1. The simplified form is equal everywhere except that excluded point.
Is the simplified answer always shorter?
Usually, but not always. Simplest form means fewest operations or a canonical form, which occasionally looks similar in length to the input while being easier to work with.
Can it simplify expressions with several variables?
Yes. It handles expressions in more than one variable, combining like terms and cancelling common factors across all of them.
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