Calculator Input
Enter coefficients from highest power to constant term. Example: 1,0,-1 means x^2 - 1.
Example Data Table
This example matches the default values already loaded into the calculator.
| Expression | Numerator Coefficients | Denominator Coefficients | Meaning |
|---|---|---|---|
| Expression 1 | 1, 1 | 1, 0, -1 | (x + 1) / (x^2 - 1) |
| Expression 2 | 2 | 1, 1 | 2 / (x + 1) |
| Expression 3 | 1, 0 | 1, -1 | x / (x - 1) |
| Expected Combined Result | (x^2 + 4x - 1) / (x^2 - 1) | ||
Formula Used
For two or more rational expressions, first find the least common denominator, often written as LCD.
N1/D1 + N2/D2 + N3/D3 = [N1(LCD/D1) + N2(LCD/D2) + N3(LCD/D3)] / LCD
After combining the numerators, simplify the final fraction by dividing both the numerator and denominator by their polynomial greatest common divisor.
How to Use This Calculator
- Choose whether you want to add two or three rational expressions.
- Enter each numerator and denominator as comma-separated coefficients.
- Keep the coefficients in descending power order.
- Set your graph range and graph step values.
- Click Calculate Sum to build the common denominator automatically.
- Review the adjusted numerators, simplified result, and graph.
- Use the export buttons to save CSV or PDF output.
FAQs
1. How should I enter polynomial coefficients?
Enter coefficients from highest degree to constant. For example, 2,-3,5 means 2x^2 - 3x + 5. A single constant uses one number only.
2. Can I add only two rational expressions?
Yes. Choose two expressions from the dropdown. The third expression fields will hide automatically, and the calculator will combine only the first two fractions.
3. What denominator method does the calculator use?
It finds the polynomial least common denominator using polynomial greatest common divisors. That keeps the denominator more efficient than simply multiplying every denominator together.
4. Does the calculator simplify the final answer?
Yes. After combining the fractions, it checks for a common polynomial factor between the final numerator and denominator, then divides both parts when simplification is possible.
5. Why do some graph values disappear?
Points disappear where a denominator becomes zero. Those x-values create vertical asymptotes, so the graph intentionally leaves gaps instead of drawing invalid points.
6. Can I use decimal coefficients?
Yes. Decimal coefficients are supported. Still, simple integer coefficients usually produce cleaner symbolic output and make the simplified rational expression easier to read.
7. What does the adjusted numerator mean?
Each fraction is rewritten over the common denominator. The adjusted numerator shows the original numerator after multiplication by the needed LCD factor.
8. What does the CSV or PDF export include?
The export includes the simplified sum, common denominator, combined numerator, simplification factor, input summary, and sampled graph data for the combined result.