Partial Fraction Calculator – Decompose complex algebraic expressions in seconds

With this tool, you can break down algebraic fractions into sums of simpler fractions by applying techniques such as the partial fractions rule.
✅ Fast and accurate – Just enter the data and get the result instantly.
✅ Avoid errors – Automatic calculation without the need for Excel sheets.
✅ Optimize your strategy – Facilitate the integration and derivation of rational expressions.
Use our calculator now and get results in seconds.

Example of Calculation with the Partial Fractions Calculator

Imagine you need to break down:
📌 (5x + 7) / [(x – 2)(x + 3)]
📐 We apply the formula: A/(x – 2) + B/(x + 3)
📊 Result: A = 3, B = 2 (for example)
This means that the original fraction can be represented as the sum of those simple fractions.
📢 Optimize your exercises with our calculator.

How Does Our Partial Fraction Calculator Work?

Our calculator follows a simple three-step process:

1️⃣ Data Entry
Enter the following values:
🔸 Numerator of the polynomial 💰 The polynomial that is on top of the fraction.
🔸 Denominator of the polynomial ⏳ The factored product of the denominator.
🔸 Variables involved 📉 “x” is generally used, but you can also use others.

Why is it important?
This process is key to simplifying complex integrals or solving differential equations.

2️⃣ Automatic Calculation
We use algebraic properties to rewrite the fraction:
📐 A/(x – a) + B/(x – b) + …

The result will allow you to work with simpler and more understandable terms.

3️⃣ Results and Recommendations
🔹 If the result is correct, you can apply it to integrals or equations.
🔹 If it cannot be factored, check if the denominator is factorable.

📢 Need to improve your math performance? 🧠 Try this free tool and save hours of manual calculations.

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What is the Partial Fraction Calculator?

It is a tool that allows you to rewrite rational expressions as sums of simple fractions, facilitating their analysis, integration, or resolution in various contexts.
👉 Increase your math accuracy and solve advanced problems more efficiently.

Learn more with these applied mathematics books

These readings will teach you how to master partial fractions, rational integrals, and fundamental algebraic methods.

1️⃣ Baldor Algebra – Aurelio Baldor
Explains step-by-step how to solve partial fractions with clarity and varied exercises.

2️⃣ Calculus of One Variable – James Stewart
Includes integration techniques with partial fractions applied to real-life contexts.

3️⃣ Advanced Mathematics for Engineering – Kreyszig
Ideal for deepening practical applications of partial fractions in engineering.

Why Use Our Partial Fraction Calculator?

✅ Speed – Get results in seconds without manual calculations.
✅ Precision – Exact formulas with no margin for error.
✅ Ease – Just enter your details and get your results instantly.
✅ Practical Application – Useful for students, teachers, and STEM professionals.

Avoid These Common Mistakes When Using the Partial Fraction Calculator

🚫 Entering a denominator that is not factorable – This prevents decomposition.
🚫 Use inconsistent variables – Make sure they match throughout the polynomial.
🚫 Do not pre-simplify the fraction – This can lead to errors in the result.

Comparison: Partial Fraction Calculator vs. Traditional Methods

✅ Fast and accurate – You don’t need to create systems of equations manually.
✅ Avoid human errors – Based on secure formulas and algorithms.
✅ Easy to use – Just enter the polynomial and get the result automatically.
✅ Accessible and free – Available online without additional software.

Frequently Asked Questions about the Partial Fraction Calculator

How to calculate partial fractions easily?
With our calculator, you just enter the numerator and denominator. The system does the rest for you.

What is the purpose of partial fraction decomposition?
It allows you to simplify integrals and solve differential equations more easily.

What formulas are used?
We use: A/(x – a) + B/(x – b) + … applying value substitution or system of equations.

What if the denominator cannot be factored?
The fraction cannot be decomposed using this method. It must be factorable.

Who can use this tool?
High school students, university students, engineers, teachers, and applied mathematicians.

Can fractions with roots or complex numbers be solved?
Yes, as long as the system can decompose the denominator correctly.

Is this tool free?
Completely free and accessible from any device.

Can I use this calculator for homework?
Yes. It's perfect for saving time and avoiding common mistakes.

How to validate the results obtained?
You can multiply the resulting partial fractions and check if the original fraction is obtained.

Does it work with higher degree polynomials?
Yes, as long as the numerator is less than the denominator and the system can factor it.