Enter a fraction, a radical, or an algebraic expression below and get it reduced to its simplest form in seconds. The calculator handles numeric fractions, square and cube roots, expressions with variables, and rational expressions built from polynomials, and it shows the steps behind every answer, not just the final result.
What Does It Mean to Simplify a Fraction, Radical, or Expression?
Simplifying means rewriting a fraction, a radical, or an expression in its shortest possible form without changing what it actually equals. The value never changes, only how it is written.
This page covers three main actions. Reducing a fraction by dividing the numerator and denominator by their greatest common factor. Combining like terms in an expression so fewer pieces are left over. And pulling perfect square or cube factors out from under a radical so the number left under the root is as small as possible.
It works a bit like scaling a recipe. If a recipe calls for 4 cups of flour and 8 cups of water, that ratio is really just 1 to 2. Writing it as 1 to 2 instead of 4 to 8 does not change how the recipe turns out, it just makes the relationship easier to read. Simplifying a fraction or an expression does the same job.
How Does the Simplify Calculator Work?
Type or paste your fraction, radical, or expression into the box above and press Simplify. The calculator reads what you entered, applies the relevant rule (finding a greatest common factor, factoring out a perfect square, combining like terms) and returns the reduced result along with the steps it took to get there.
A few things worth knowing before you type:
● Use ^ for exponents, so x squared is written as x^2
● Fractions can be entered with a forward slash, such as 3/4
● Parentheses work as expected, so 2(x+4) means 2 multiplied by the group (x+4)
The calculator works with plain numbers as well as expressions that include variables like x or y.
What Types of Expressions Can the Calculator Simplify?
The table below shows the four categories handled on this page, with one example of each.
Expression Type | Example Input | Simplified Output |
Fraction | 24/108 | 2/9 |
Radical (square root) | √72 | 6√2 |
Algebraic expression | 2(5x+4) - 3x | 7x + 8 |
Rational expression | (3x² + 6x)/3 | x² + 2x |
How to Simplify Fractions With the Calculator
A fraction is fully simplified when its numerator and denominator share no common factor other than 1. The fastest way to get there is to find the greatest common factor, or GCF, of both numbers and divide each one by it.
Example: simplify 24/108
1. Find the GCF of 24 and 108. In this case, the largest number that divides both evenly is 12.
2. Divide the numerator by 12: 24 ÷ 12 = 2
3. Divide the denominator by 12: 108 ÷ 12 = 9
4. The simplified fraction is 2/9. Since 2 and 9 share no common factor, the fraction is fully reduced.
If you land on an improper fraction, one where the numerator is larger than the denominator, the calculator also shows it as a mixed number. For example, 13/3 simplifies to 4 1/3.
How to Simplify Radical Expressions (Square Roots)
Simplifying a radical means pulling any perfect square, or perfect cube for cube roots, out from under the root symbol, leaving the smallest possible number behind.
Example: simplify √72
1. Break 72 into factors, looking for a perfect square. 72 = 36 × 2, and 36 is a perfect square.
2. Apply the product rule for radicals: √(a×b) = √a × √b. So √72 = √36 × √2.
3. Take the square root of the perfect square: √36 = 6.
4. The simplified form is 6√2.
If a variable sits under an even-index radical, like √(x²), the technically correct result is the absolute value of x, written |x|, since x could be negative. Most algebra courses assume variables are positive unless stated otherwise, in which case √(x²) simplifies to just x.
How to Simplify Algebraic Expressions With Variables
Three techniques cover most algebraic simplification: combining like terms, applying the distributive property, and using exponent rules.
Combining like terms means adding or subtracting terms that share the same variable raised to the same power. 3x and 5x are like terms and combine to 8x, but 3x and 3x² are not, since the exponents are different.
The distributive property clears parentheses by multiplying the term outside by each term inside: 2(x+4) becomes 2x + 8.
Exponent rules simplify repeated multiplication or division of the same base. Dividing x^5 by x^2 gives x^3, since dividing subtracts the exponents.
Example: simplify 2(5x+4) - 3x
1. Distribute the 2: 2(5x+4) = 10x + 8
2. Rewrite the full expression: 10x + 8 - 3x
3. Combine the like terms, 10x and -3x: 10x - 3x = 7x
4. The simplified expression is 7x + 8
Simplify Calculator Examples With Step by Step Solutions
A quick reference for three common cases, one fraction, one radical, and one algebraic expression, so you can see the pattern before trying your own problem in the calculator above.
Starting Expression | Rule Applied | Simplified Result |
4/8 | Divide by the GCF (4) | 1/2 |
√48 | Factor out the perfect square (16) | 4√3 |
3x + 5x - 2 | Combine like terms | 8x - 2 |
What Common Mistakes Cause Wrong Simplified Answers?
Most wrong answers come from a handful of repeat mistakes rather than a real gap in understanding. These are the ones worth double checking before trusting a simplified result.
Mistake | What Goes Wrong | Correct Approach |
Combining unlike terms | Treating 3x and 2x² as the same kind of term | Only combine terms with matching variables and matching exponents |
Forgetting to distribute a negative sign | Writing 5-(x+3) as 5-x+3 | Distribute the negative across every term inside: 5-x-3 |
Canceling terms instead of factors | Crossing out the x in (x²+x)/x directly | Factor first, x(x+1)/x, then cancel the shared factor to get x+1 |
Ignoring order of operations | Solving 3+4×2 as 14 | Multiply before adding: 3+4×2 = 11 |
Dropping parentheses too early | Removing grouping before checking the sign in front of it | Check for a negative sign or multiplication first, then remove the parentheses |
Confusing simplifying with solving | Expecting a numeric answer with an equals sign | Simplifying only rewrites an expression, it does not solve for a variable |
There is one extra case worth knowing if you are working with rational expressions, meaning fractions with polynomials on top and bottom. Canceling a shared variable factor can technically remove a value that was not allowed in the original expression. For example, (x²+x)/x simplifies to x+1, but the original expression was never defined at x=0, since that would mean dividing by zero. The simplified version does not carry that restriction unless it is noted separately.
How Does Simplifying Connect to Solving Equations and Graphing?
Simplifying is usually the first move, not the last one. Once an expression is reduced to its simplest form, solving an equation for a variable becomes easier because there are fewer terms to work through. The same applies to graphing, a simplified function is faster to plot and easier to read since its structure is clearer. If your next step is finding the value of x rather than just cleaning up an expression, the tools below can take it from there.
Fraction Calculator: How Do You Add, Subtract, Multiply, and Divide Fractions?
Once a fraction is simplified, you will often need to combine it with another one, whether that means adding two fractions with different denominators or multiplying a pair together. The fraction calculator handles full fraction arithmetic and automatically reduces the result, so there is no need to simplify a second time by hand.
GCF Calculator: How Do You Find the Greatest Common Factor of Two Numbers?
The greatest common factor is the method behind every fraction reduction on this page, but sometimes the factor itself is what you need, not a reduced fraction, for example when working through a word problem or comparing ratios. The GCF calculator finds that number directly.
Square Root Calculator: How Do You Simplify or Estimate a Radical in More Depth?
This page covers how to pull perfect squares out of a radical, but if a decimal approximation or a higher-index root is what you are after, the square root calculator goes further, using the same factoring logic explained above.
Algebra Calculator: How Do You Solve an Equation Step by Step After Simplifying?
Simplifying and solving are related but not the same thing. Simplifying rewrites an expression, solving isolates a variable using an equals sign. Once an expression is reduced, the algebra calculator can carry it through to a full solution.
Factoring Calculator: How Do You Factor a Polynomial Instead of Just Simplifying It?
Factoring and simplifying overlap, but they are not identical. Factoring breaks an expression into multiplied parts, while simplifying just reduces it to its shortest form. For a fully factored polynomial, say for solving a quadratic equation, the factoring calculator is built for that.
Trigonometric Expression Calculator: How Do You Simplify Trig Identities?
Expressions built from sine, cosine, and tangent follow their own set of identities and simplification rules, separate from the fraction and algebra rules covered on this page. For a trig identity, the trigonometry calculator is the better fit.