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Reduce The Following Rational Expression to Lowest Terms Calculator

Reviewed by Calculator Editorial Team

This calculator helps you reduce rational expressions to their lowest terms. Rational expressions are fractions where both the numerator and denominator are polynomials. Reducing them to lowest terms means simplifying the fraction by canceling out common factors in both the numerator and denominator.

How to Use This Calculator

To use the calculator, follow these steps:

  1. Enter the numerator of your rational expression in the first input field.
  2. Enter the denominator of your rational expression in the second input field.
  3. Click the "Calculate" button to reduce the expression to lowest terms.
  4. Review the simplified result and the step-by-step solution.

The calculator will display the simplified form of your rational expression and show the steps used to simplify it.

How to Reduce Rational Expressions

Reducing a rational expression to lowest terms involves these key steps:

  1. Factor both the numerator and denominator completely.
  2. Identify and cancel out any common factors in the numerator and denominator.
  3. Write the simplified expression.

Remember that you can only cancel out factors that are common to both the numerator and denominator. Also, be careful not to cancel out any factors that would make the denominator zero.

For example, to reduce (x² + 3x + 2)/(x² - x - 6):

  1. Factor the numerator: x² + 3x + 2 = (x + 1)(x + 2)
  2. Factor the denominator: x² - x - 6 = (x + 3)(x - 2)
  3. There are no common factors, so the expression is already in lowest terms.

Worked Examples

Example 1: Simple Reduction

Original expression: (2x + 4)/(x + 2)

Step 1: Factor the numerator: 2x + 4 = 2(x + 2)

Step 2: The denominator is already factored: x + 2

Step 3: Cancel out the common factor (x + 2)

Simplified expression: 2

Example 2: More Complex Reduction

Original expression: (x² - 4)/(x² - 2x - 3)

Step 1: Factor the numerator: x² - 4 = (x + 2)(x - 2)

Step 2: Factor the denominator: x² - 2x - 3 = (x + 1)(x - 3)

Step 3: There are no common factors, so the expression is already in lowest terms.

Simplified expression: (x² - 4)/(x² - 2x - 3)

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 - 2) and (x² + 3x + 2)/(x² - 5).

How do I reduce a rational expression to lowest terms?

To reduce a rational expression, factor both the numerator and denominator completely, then cancel out any common factors. The simplified form is the result.

Can I cancel out any factors I want?

No, you can only cancel out factors that are common to both the numerator and denominator. Also, be careful not to cancel out factors that would make the denominator zero.

What if the numerator and denominator have no common factors?

If there are no common factors, the rational expression is already in its lowest terms and cannot be simplified further.