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Add The Following Rational Expressions Calculator

Reviewed by Calculator Editorial Team

This calculator helps you add two rational expressions by finding a common denominator and combining the numerators. Rational expressions are fractions where both the numerator and denominator are polynomials. The result is simplified to its lowest terms.

How to Use This Calculator

To add rational expressions using this calculator:

  1. Enter the first rational expression in the format (a/b)
  2. Enter the second rational expression in the format (c/d)
  3. Click "Calculate" to see the result
  4. Review the step-by-step solution
  5. Use the "Reset" button to clear the form

The calculator will show you the final simplified result and the detailed steps used to arrive at the answer.

Formula for Adding Rational Expressions

To add two rational expressions (a/b) + (c/d), follow these steps:

  1. Find the Least Common Denominator (LCD) of b and d
  2. Rewrite each fraction with the LCD as the denominator
  3. Combine the numerators
  4. Simplify the resulting fraction

Mathematical Formula

(a/b) + (c/d) = [(a × d) + (c × b)] / (b × d)

The LCD is the smallest number that both denominators divide into evenly. The simplified result is obtained by dividing both the numerator and denominator by their greatest common divisor (GCD).

Worked Examples

Example 1: (1/2) + (1/3)

  1. LCD of 2 and 3 is 6
  2. Rewrite fractions: (3/6) + (2/6)
  3. Combine numerators: 3 + 2 = 5
  4. Result: 5/6

Example 2: (2/5) + (3/10)

  1. LCD of 5 and 10 is 10
  2. Rewrite fractions: (4/10) + (3/10)
  3. Combine numerators: 4 + 3 = 7
  4. Result: 7/10

Tip

Always simplify the result by dividing numerator and denominator by their GCD to get the most reduced form.

Frequently Asked Questions

What is a rational expression?
A rational expression is a fraction where both the numerator and denominator are polynomials. Examples include (x+1)/x and (2x+3)/(x²-1).
Why do I need a common denominator?
A common denominator allows you to combine the fractions by adding their numerators. The LCD is the smallest number that both denominators divide into evenly.
How do I simplify the result?
Divide both the numerator and denominator by their greatest common divisor (GCD) to get the simplest form of the fraction.
What if the denominators are the same?
If the denominators are identical, you can simply add the numerators and keep the same denominator. For example, (1/4) + (2/4) = 3/4.