How to Divide Rational Expressions

Rational expressions are also known as algebraic expressions. A rational expression is the quotient of two polynomials. It is important to remember that the divisor can not be zero. A quotient is the answer to a division problem. Polynomials are expressions with the sum of powers with at least one variable multiplied by coefficients.

Instructions

How to Divide Rational Expressions

1. Multiply by the reciprocal by flipping the divisor. The divisor is 10x2/4. The reciprocal of the divisor is 4/10x2. Thus, 5x2/2 x 4/10x2 are the factors. Original problem: 5x2/2÷10x2/4

2. Multiply the numerators. 5x2 and 4 are the numerators. 5x2 times 4 is 20x2. 20x2 is the new numerator.

3. Multiply the denominators. 2 and 10x2 are the denominators. 2 multiplied by 10x2 is 20x2. 20x2 is the new denominator.

4. Put the new numerator in step 2 (20x2) and the new denominator in step 3 (20x2) together: 20x2/ 20x2.

5. Simplify, if needed. 20x2/ 20x2=1 because any number divided by itself is 1. Therefore, 1 is the answer.

Tips & Warnings

• Note that any number after a letter is an exponent:10x2 IS 10x to the 2ndpower for instance or 5x2 is 5x to the 2nd power.