Adding and Subtracting Rational Expressions Calculator

A rational expression is an expression such that it can be expressed as the quotient or fraction p/q or simply quotient of two polynomials. It means both the numerator and denominator are polynomials.

What is Adding and Subtracting Rational Expressions Calculator?

'Cuemath's Adding and Subtracting Rational Expressions Calculator' is an online tool that helps to calculate the sum and difference for given rational expressions. Cuemath's online Adding and Subtracting Rational Expressions Calculator helps you to calculate the sum and difference for given rational expressions in a few seconds.

How to Use Adding and Subtracting Rational Expressions Calculator?

Please follow the steps below on how to use the calculator:

• Step 1: Enter the numerator and denominator of rational expressions in the given input box.
• Step 2: Click on the "Addition" or 'Subtraction" button depending on the requirement.
• Step 3: Click on the "Calculate" button to find the sum and difference for given rational expressions.
• Step 4: Click on the "Reset" button to reset the fields and find the sum and difference for different rational expressions.

How to Find Adding and Subtracting Rational Expressions?

Adding of Rational Expressions: We can add the numerators and the denominators and then simplify the product.

• If the denominator values are the same, add the numerators and express the rational expression in its simplest form.
• If the denominator values are different, find the LCM of the denominators to make them equal and then add the numerators. 

For example, Add 4 / 5 and 9 / 5 = 4 / 5 + 9 / 5 = 13 / 5 . The same can be applied to rational expressions.

Subtracting Rational Expressions: We can subtract the numerators and the denominators and then simplify the product.

• If the denominator values are the same, subtract the numerators and express the rational expression in its simplest form.
• If the denominator values are different, find the LCM of the denominators to make them equal and then subtract the numerators. 

For example, Subtract 2 / 3 and 5 / 9 = 2 / 3 - 9 / 5 = -17 / 15 .The same can be applied to rational expressions.

Solved Example:

Find the sum of two given rational expressions (x + 3) / (x + 1) and (x + 2) / (x + 1)

Solution:

Add (x + 3) / (x + 1) and (x + 2) / (x + 1)

= ((x + 3) + (x + 2)) / (x + 1)

= (2x + 5) / (x + 1)

Similarly, you can try the calculator to find adding and subtracting rational expressions for

• Add 4x² / 9 and 3x³ / 4
• Subtract 2x² / 5 and 4x / 6