Complex Algebraic Rational Simplifier & Verifier
Verify algebraic simplifications by substituting values. Check if two complex rational expressions are equivalent instantly. Includes a logic library reference.
Equivalence Checker
Enter expressions using 'x' as the variable. (e.g., (x^2 - 1)/(x - 1))
About
Simplifying complex algebraic expressions—especially those involving nested fractions, roots, and high-degree polynomials—is prone to human error. A single misplaced minus sign can invalidate pages of derivation. This tool acts as a rigorous 'Verification Engine'.
Instead of just guessing, it allows you to input your original expression and your simplified result. The engine then runs a numerical substitution algorithm across multiple random points (avoiding asymptotes) to mathematically prove or disprove equivalence with high probability. It is an essential tool for Calculus students checking derivatives or integrals simplified by hand.
Formulas
The verification logic relies on the Identity Theorem. If two continuous functions f(x) and g(x) yield the same result for a set of random values within their domain, they are likely equivalent.
Reference Data
| Identity Type | Expression | Expanded/Simplified Form |
|---|---|---|
| Difference of Squares | a^2 - b^2 | (a - b)(a + b) |
| Perfect Square Trinomial | (a + b)^2 | a^2 + 2ab + b^2 |
| Difference of Cubes | a^3 - b^3 | (a - b)(a^2 + ab + b^2) |
| Sum of Cubes | a^3 + b^3 | (a + b)(a^2 - ab + b^2) |
| Square of Trinomial | (a+b+c)^2 | a^2+b^2+c^2+2ab+2bc+2ca |
| Rational Addition | 1/a + 1/b | (a+b)/ab |
| Nested Fraction | (a/b) / (c/d) | ad / bc |