Fraction Equation Solver
Solves linear equations containing fractions by calculating the LCM and clearing denominators. Explicitly shows the multiplication step.
Solve: (1/A)x + (1/B) = (1/C)
About
Equations with fractions, known as rational equations, intimidate many students due to the complexity of finding a common denominator. The most efficient strategy is to eliminate fractions entirely in the first step. This tool automates the process of finding the Least Common Multiple (LCM) of all denominators. It then multiplies every term by this LCM. This transforms a messy fractional equation into a clean linear one with integer coefficients, reducing the cognitive load and likelihood of arithmetic errors.
Formulas
To solve xa + yb = c:
1. Find LCM(a, b) = L
2. Multiply entire eq by L:
L ⋅ xa + L ⋅ yb = L ⋅ c
This results in integer terms.
Reference Data
| Fraction Type | Example | LCM Strategy | Goal |
|---|---|---|---|
| Simple | x2 + 13 = 5 | Multiply by 6 | Integer Coeffs |
| Variable Denom | 2x + 1 = 4 | Multiply by x | Linear Eq |
| Complex | 1x+1 = 2 | Multiply by (x+1) | Isolate x |
| Mixed | 1 12 x | Convert to Improper | Standard Form |
| Decimal | 0.5x | Multiply by 10 | Remove Point |
| Negative | −25 | Keep Sign | Maintain Value |
| Zero Denom | 10 | Undefined | Error |
| Unit | 1n | Multiply by n | Unity |