Calculator Form
Enter one-variable polynomial expressions. Supported symbols: +, -, *, ^, parentheses, and implicit multiplication like 2x(x+1).
Example Data Table
| Numerator | Denominator | Simplified Form | Restriction |
|---|---|---|---|
| x^2 - 1 | x^2 - x | (x + 1) / x | x ≠ 0, 1 |
| 2x^2 + 6x | 4x | (x + 3) / 2 | x ≠ 0 |
| x^2 + 5x + 6 | x + 2 | x + 3 | x ≠ -2 |
| x^2 - 9 | x^2 - 6x + 9 | (x + 3) / (x - 3) | x ≠ 3 |
Formula Used
The calculator expands each polynomial, combines like terms, and finds the greatest common divisor of the numerator and denominator.
Core ideas applied during simplification:
- Expand powers and products into standard polynomial form.
- Use polynomial long division inside the Euclidean algorithm.
- Cancel only factors common to both numerator and denominator.
- Keep original denominator restrictions even after cancellation.
How to Use This Calculator
- Enter the numerator expression using one variable.
- Enter the denominator expression with the same variable.
- Choose the variable symbol and decimal precision.
- Press Simplify Expression to reduce the fraction.
- Review the common factor, coefficient tables, and domain note.
- Use the CSV or PDF buttons to save the result.
FAQs
1. What expressions does this calculator accept?
It accepts one-variable polynomial expressions with integers, parentheses, powers, multiplication signs, and implicit multiplication such as 3x(x+2).
2. Does it preserve excluded values after cancellation?
Yes. Even when a factor cancels, the calculator keeps restrictions from the original denominator so the final domain stays mathematically correct.
3. Can it simplify constants and polynomial factors together?
Yes. It removes common numeric content and common polynomial factors, then normalizes the final denominator sign when needed.
4. Does it support decimals or multiple variables?
No. This version focuses on exact one-variable polynomial simplification with integer coefficients for reliable symbolic reduction.
5. Why does the result sometimes stay as a fraction?
That happens when numerator and denominator still share no removable factor. The expression is already simplified under the given rules.
6. What if my denominator becomes zero?
The calculator stops and shows an input issue because a zero denominator makes the rational expression undefined.
7. How are domain notes estimated for quadratics?
For linear and quadratic denominators, the tool computes exact or approximate real roots and reports the excluded values directly.
8. What do the CSV and PDF exports include?
They capture the original expressions, common factor, simplified form, and domain summary so you can document or share results quickly.