This calculator works with rational equations, that is, equations with a quotient of polynomials on one or both sides. For a single missing term between two fractions, such as 3/4 = x/20, the find a missing fraction value calculator is more direct; here x can be anywhere, including the denominator.
Worked example: x/2 + 1/3 = 5/6
Find the value of x that makes the equality true. The denominators are 2, 3 and 6.
- Find the common denominator. The LCM (least common multiple) of 2, 3 and 6 is 6.
- Multiply both sides by 6. 6 × (x/2) + 6 × (1/3) = 6 × (5/6), which is 3x + 2 = 5.
- Solve for x. 3x = 3, so x = 1.
- Check in the original. With x = 1 the left side is 1/2 + 1/3 = 5/6, the same as the right side.
Solution: x = 1.
Check. 1/3 = 0.333… and 5/6 = 0.8333…, and the sum of 0.5 and 0.333… gives 0.8333…. There are no restrictions here, because the denominators are numbers.
What changes when x is in the denominator
Clearing denominators means multiplying by an expression with x, and that can let in values the original equation does not allow. That is why you first write down which values make any denominator zero, and only then solve.
| Equation | Restriction | Result |
|---|---|---|
| 2/(x − 1) = 3/(x + 2) | x ≠ 1 and x ≠ −2 | One solution: x = 7, because 2/6 = 3/9 = 1/3 |
| (x² − 1)/(x − 1) = 2 | x ≠ 1 | None: it reduces to x + 1 = 2, and x = 1 is excluded |
| x + 1/x = 5/2 | x ≠ 0 | Two: 2x² − 5x + 2 = 0 gives x = 1/2 and x = 2 |
| (x + 3)/(x + 3) = 1 | x ≠ −3 | Identity: true for every x except −3 |
The table sums up the three possible endings: one or two solutions, none, or infinitely many. In the third row, both solutions are valid because only 0 is excluded; for example, 1/2 + 2 = 5/2.
How to enter the equation
Use a single equals sign and put parentheses around every numerator or denominator with several terms, for example (x^2-1)/(x-1)=2. Always write the product, as 2*x and not 2x.
This calculator accepts one equality and the letter x, with no systems, inequalities, other unknowns or roots in the input equation. If you need those cases, other pages cover them. For inequalities such as 1/x > 2, see inequalities with fractions, which require a sign analysis. For two equations with two unknowns, see systems of equations with fractions. And if you only want to simplify an expression with no equals sign, use algebraic fractions, which also keep the restrictions. When the equality is between two numerical ratios, the proportions calculator solves for the unknown term.
Source: English Wikipedia, article Equation, section “Properties”, which notes that applying a function to both sides of an equation can introduce extraneous solutions (accessed October 17, 2026).
Frequently asked questions
How do I enter a fraction times x, like five eighths of x?
Put the fraction in parentheses and write the multiplication sign before the x, as in (5/8)×x + 1 = 11, which gives x = 16. Do the same with negative coefficients, (-3/7)×x, instead of -3/7x: without the multiplication sign, the calculator rejects the input and shows an error. The asterisk and the middle dot also work.
How do I read a result with sqrt?
sqrt(13) is √13, a root that does not simplify and is left exact. For x + 3/x = 5, multiplying by x gives x² − 5x + 3 = 0, with discriminant 25 − 12 = 13. The solutions are x = (5 − √13)/2 and x = (5 + √13)/2, and neither is 0, so both are valid.
What do I do if the calculator rejects the equation because of its degree?
Move everything to one side so the subtraction simplifies before the denominators are cleared. x^2/(x-6) = 36/(x-6) comes out as degree 3 and is rejected, but x^2/(x-6) - 36/(x-6) = 0 reduces to x + 6 = 0, with solution x = −6; x = 6 is excluded.
Why is there only one solution when the equation has an x²?
There are two reasons. It can be a double root, when the discriminant is 0: x + 9/x = 6 reduces to x² − 6x + 9 = 0 and gives only x = 3. Or one of the two roots makes a denominator zero and is discarded: x²/(x − 1) − 1/(x − 1) = 0 reduces to x² = 1; of x = 1 and x = −1, only x = −1 is valid.