Find The Product of The Following Rational Algebraic Expressions Calculator

This calculator helps you find the product of two rational algebraic expressions. Rational expressions are fractions where both the numerator and denominator are polynomials. Multiplying them involves multiplying the numerators together and the denominators together, then simplifying the result.

How to Use This Calculator

To find the product of two rational algebraic expressions:

Enter the first rational expression in the format (a/b) where a and b are polynomials
Enter the second rational expression in the same format
Click "Calculate" to see the product
The result will show the multiplied form and the simplified form if possible

For example, if you enter (x+1)/(x-2) and (x-3)/(x+4), the calculator will show you the step-by-step multiplication and simplification.

Formula for Multiplying Rational Expressions

The general formula for multiplying two rational expressions is:

(a/b) × (c/d) = (a × c)/(b × d)

Where:

a and c are the numerators of the two expressions
b and d are the denominators of the two expressions

After multiplying, you should simplify the resulting fraction by factoring and canceling common terms in the numerator and denominator.

Worked Example

Let's multiply (2x+3)/(x-1) and (x+4)/(2x-5):

Multiply the numerators: (2x+3)(x+4) = 2x² + 11x + 12
Multiply the denominators: (x-1)(2x-5) = 2x² - 7x + 5
Combine to get (2x² + 11x + 12)/(2x² - 7x + 5)
Check for common factors - none in this case

The final product is (2x² + 11x + 12)/(2x² - 7x + 5).

Frequently Asked Questions

What is a rational algebraic expression?: A rational algebraic expression is a fraction where both the numerator and denominator are polynomials. Examples include (x+2)/(3x-1) or (2x²-5)/(x+4).
How do I multiply rational expressions?: Multiply the numerators together and the denominators together, then simplify the resulting fraction by factoring and canceling common terms.
What if the expressions have common factors?: If there are common factors in the numerator and denominator, you can cancel them out after multiplying, but only if they don't make the denominator zero.
Can I multiply more than two rational expressions?: Yes, you can multiply any number of rational expressions by multiplying all the numerators together and all the denominators together, then simplifying.
What if the denominator becomes zero?: The product is undefined if any value of x makes the denominator zero. You should note these restrictions in your final answer.