Equations with fractions solver

Equations With Fractions Calculator

Solve for x when a linear equation contains one or several fractions with constant denominators, then check the result in the original equation.

Try an example

Which equations with fractions are supported?

I use this page for linear equations where the denominators are numbers, including x/3 + 5 = 12, x/4 + x/2 = 9, and (2x + 1)/3 + (x - 2)/4 = 5.

If x appears in a denominator, the problem is a rational equation instead. I send those inputs to the Rational Equation Calculator so domain restrictions are preserved.

How I clear constant denominators

A constant denominator only scales a linear expression, so I can combine the fractional coefficients or multiply through by a common numeric denominator without changing the solution set.

After x is isolated, the calculator substitutes the result into the exact equation that was entered rather than checking only the simplified line.

Try an example

Type or paste an equation, solve it, inspect the transformations, and use verification and the graph instead of relying on the final value alone.

x/3 + 5 = 12
x/4 + x/2 = 9
(2x + 1)/3 + (x - 2)/4 = 5
2x/3 - x/5 = 7

Worked examples

Follow the same steps the calculator uses for three equations in this category.

x/3 + 5 = 12

x = 21

  1. Subtract 5 from both sides

    0.333333333333x+5=12 → 0.333333333333x=7

  2. Divide both sides by 0.333333333333

    0.333333333333x=7 → x=21

Verified

x/4 + x/2 = 9

x = 12

  1. Divide both sides by 0.75

    0.75x=9 → x=12

Verified

(2x + 1)/3 + (x - 2)/4 = 5

x = 62/11

  1. Add 0.166666666667 to both sides

    0.916666666667x-0.166666666667=5 → 0.916666666667x=5.166666666667

  2. Divide both sides by 0.916666666667

    0.916666666667x=5.166666666667 → x=5.636363636364

Verified

Common mistakes

  • This variable-denominator form is outside the supported rational-equation patterns.
  • This equation type is not supported yet.
  • Substitute each answer into the original equation and compare both sides.

Frequently asked questions

What does this calculator support?
Solve linear equations such as x/3 + 5 = 12 when denominators are constants.
How does it verify an answer?
Substitute each answer into the original equation and compare both sides.
Which equations are outside the supported range?
Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.

Verification

Substitute each answer into the original equation and compare both sides.

Current solver scope

Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.

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