Algebraic Fraction Simplifier
Simplify complex rational expressions by factoring polynomials. Visualize the cancellation of common factors in the numerator and denominator.
About
Simplifying rational expressions is a critical skill in algebra that mimics the simplification of numerical fractions. The process requires breaking down both the numerator and denominator into their prime polynomial factors. Students often mistakenly cancel terms that are part of a sum, such as cancelling x in x + 1x, which is mathematically invalid.
This tool enforces the strict rule that cancellation can only occur between factors (multiplicative terms). It visually demonstrates the "striking out" of matching binomials or monomials, providing a clear visual aid for understanding how the expression reduces to its lowest terms.
Formulas
Simplification relies on the Fundamental Theorem of Arithmetic applied to polynomials.
Where C(x) is the greatest common divisor (GCD) of the numerator and denominator.
Reference Data
| Numerator | Denominator | Factors | Simplified |
|---|---|---|---|
| x2 − 9 | x + 3 | (x−3)(x+3) / (x+3) | x − 3 |
| x2 + 5x + 6 | x + 2 | (x+3)(x+2) / (x+2) | x + 3 |
| 2x | 4x2 | 2⋅x / 2⋅2⋅x⋅x | 12x |
| x3 − x | x − 1 | x(x−1)(x+1) / (x−1) | x(x+1) |