Rational Expressions Simplifier
Simplify algebraic fractions by factoring polynomials and canceling common terms. Handles linear and quadratic expressions.
Factorized Form:
Simplified Form:
About
Rational expressions are essentially fractions where the numerator and denominator are polynomials. Simplifying them is a critical skill in algebra that involves factoring (breaking expressions into products of simpler terms) and then canceling any factors that appear in both the top and bottom. This tool identifies common patterns such as the Difference of Squares (a2 − b2) and standard quadratic trinomials (x2 + bx + c) to reduce expressions to their simplest form.
algebra
rational expressions
polynomials
factorization
math
Formulas
The simplifier looks for factors P(x) such that:
A(x)B(x) = P(x) ⋅ A'(x)P(x) ⋅ B'(x) = A'(x)B'(x)
Logic requires the polynomial be factorable over integers.
Reference Data
| Pattern Name | Formula | Example |
|---|---|---|
| Difference of Squares | a2 − b2 = (a−b)(a+b) | x2 − 9 = (x−3)(x+3) |
| Perfect Square | a2 + 2ab + b2 = (a+b)2 | x2 + 6x + 9 = (x+3)2 |
| GCF Extraction | ax + ay = a(x+y) | 5x + 10 = 5(x+2) |
| Sum of Cubes | a3 + b3 = (a+b)(a2−ab+b2) | x3 + 8 |
Frequently Asked Questions
This tool focuses on standard textbook cases: linear expressions and quadratic trinomials that can be factored into integers. Complex polynomials requiring the quadratic formula for irrational roots are generally left as-is.
Use the "^" symbol. For x squared, type "x^2". For x cubed, type "x^3". The tool automatically parses standard string inputs.
An excluded value is a number for x that would make the denominator zero. Even if you cancel out a term like (x-2), x still cannot equal 2 in the original function domain.
If the expression didn't change, the numerator and denominator share no common factors. The expression is already in its simplest form.