Calculator
Example Data Table
| Example | Term One | Term Two | Extra Term | Purpose |
|---|---|---|---|---|
| Basic unlike denominators | (2x+3)/(x+1) | (x-4)/(x-2) | None | Builds a product common denominator. |
| Subtraction included | (x)/(x+5) | −(3)/(x-1) | None | Checks sign handling. |
| Three rational expressions | (1)/(x+1) | (2)/(x-1) | −(1)/(x^2-1) | Tests a longer numerator combination. |
| Quadratic denominator | (x+2)/(x^2-4) | (5)/(x+2) | None | Shows domain warnings for roots. |
Formula Used
Two expressions:
A/B + C/D = (AD + CB) / BD
Multiple expressions:
Σ sᵢNᵢ/Dᵢ = [Σ sᵢNᵢ ΠDⱼ] / ΠDᵢ, where j ≠ i
The calculator multiplies all entered denominators to form a common denominator. Then it scales every numerator by the missing denominator factors. Finally, it adds or subtracts the adjusted numerators.
How to Use This Calculator
- Enter each numerator as a polynomial, such as
2x+3. - Enter each denominator as a polynomial, such as
x^2-1. - Select plus or minus signs for extra terms.
- Leave unused term boxes empty.
- Choose a test x-value and graph range.
- Press Find Sum.
- Review the combined numerator, common denominator, domain notes, and graph.
- Use CSV or PDF export for saving the result.
About Adding Rational Expressions
What the calculator does
A rational expression is a fraction built from polynomials. The numerator sits above the denominator. The denominator cannot equal zero. Adding these expressions requires a shared denominator. This shared base lets every term use the same lower polynomial. The calculator reads each polynomial part. It then builds a common denominator and combines the adjusted numerators.
Why the denominator matters
Unlike normal numbers, algebraic fractions carry restrictions. A value of x may make a denominator zero. That value must be excluded from the domain. The calculator lists real restrictions for linear and quadratic denominators. Higher degree denominators are flagged for separate solving. This helps users avoid invalid answers.
How the work is organized
The tool first parses each numerator and denominator. It expands products internally. For each expression, the numerator is multiplied by every other denominator. A subtraction sign changes the adjusted numerator before addition. The final result is displayed as one rational expression. The graph uses the same combined numerator and denominator.
Best use cases
Use this page for homework checks, lesson examples, worksheet building, and quick algebra review. It supports decimals, fraction coefficients, constants, linear terms, and polynomial powers like x^2. Results include steps, a sample evaluation, domain guidance, a graph, and export buttons. Always review the factor form when your class requires full simplification by cancellation.
FAQs
What is a rational expression?
A rational expression is a fraction with polynomial expressions in the numerator, denominator, or both. The denominator cannot be zero.
How does this calculator add rational expressions?
It forms a common denominator, adjusts each numerator, applies the selected signs, and combines the numerator terms into one expression.
Can I subtract rational expressions?
Yes. Choose the minus sign before a term. The calculator multiplies that adjusted numerator by negative one before combining terms.
Which polynomial format should I enter?
Use plain polynomial text, such as x+1, 2x-3, x^2-4, or 1/2x+5. Do not enter full fractions in one field.
Does the calculator find domain restrictions?
It lists restrictions for linear and quadratic denominators. For higher powers, it tells you to solve the denominator equation separately.
Does it cancel common factors?
The calculator gives the combined expanded form. For classroom factor cancellation, factor the final numerator and denominator after reviewing the result.
Why is the graph broken sometimes?
The graph skips points where the denominator is zero or where values become too large. These breaks often show vertical asymptotes.
Can I export my answer?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a printable summary of the expression and answer.