Rational Equation Solver
Solve rational algebraic equations, identify common denominators, and detect excluded values (domain restrictions). Step-by-step logic for standard forms.
Solve for form: Ax + B + C = Dx + E
About
Rational equations involve fractions where the numerator and denominator are polynomials. Solving these requires finding a Common Denominator to eliminate fractions, converting the problem into a standard linear or quadratic equation. A critical and often overlooked step is identifying excluded values. These are input values that would cause division by zero, rendering the expression undefined.
This solver handles equations in the form of Ax + B + C = Dx + E. It checks the domain restrictions automatically, ensuring that the computed solution is valid and not an extraneous root.
Formulas
To solve rational equations, multiply every term by the Least Common Denominator (LCD). For the form:
ax + b = c
We multiply both sides by (x + b), provided x ≠ −b:
a = c(x + b)
Reference Data
| Expression Type | Example | Excluded Values (x ≠) |
|---|---|---|
| Simple Reciprocal | 1x = 5 | 0 |
| Linear Denominator | 2x − 3 = 4 | 3 |
| Complex Rational | xx + 2 = 1x − 2 | -2, 2 |
| Quadratic Denom. | 3x2 − 1 = 1 | -1, 1 |