Partial Fractions Calculator

Using the Partial Fractions Calculator: Step-by-Step Guide

Introduction

This guide will assist you in using the Partial Fractions Calculator to decompose a given fraction into its partial fractions. The calculator requires specific input values and offers different types of decomposition. Follow these steps to successfully carry out the decomposition.

Step 1: Enter the Numerator Coefficient

Begin by entering the coefficient of the numerator. This is the value that sits on top of the fraction you wish to decompose.

• Locate the input field labeled Numerator Coefficient.
• Enter a whole number within the range of -1000 to 1000.
• Ensure this field is completed, as it is required for the calculation.

Step 2: Input the Denominator Coefficients

The denominator of your fraction is composed of two separate factors. You will need to input these coefficients individually.

• In the First Denominator Factor field, input the coefficient for the first component of your denominator, ensuring it is between -1000 and 1000.
• Proceed to the Second Denominator Factor field and enter the coefficient for the second component, also between -1000 and 1000.

Step 3: Select the Decomposition Type

You have the option to choose between linear and quadratic factors for your decomposition.

• Locate the Decomposition Type selection field.
• Choose either Linear Factors (ax + b) or Quadratic Factors (ax² + bx + c) depending on your decomposition preference.

Step 4: View Partial Fractions Results

Once you’ve entered the necessary values and selection, the calculator will process your input to provide partial fraction results.

• The First Partial Fraction is computed using the formula: (numerator * denominator2) / (denominator1 * (denominator1 – denominator2)). This result will be displayed with four decimal places.
• The Second Partial Fraction will also appear, calculated by: (numerator * denominator1) / (denominator2 * (denominator2 – denominator1)).

Step 5: Review Combined Result and Verification

The calculator provides a combined evaluation of your partial fractions alongside a verification check to ensure accuracy.

• The Combined Result shows the summed value of the first and second partial fractions. This is useful for assessing the overall decomposition.
• A Verification Check is included, comparing your original fraction value (numerator / product of denominator1 and denominator2) with the partial fractions outcome.

Ensure all values are in place and interpreted correctly to achieve precise and useful decompositions with the Partial Fractions Calculator.