What is a rational expression? A rational expression is a fraction made up of polynomials. Both the numerator and the denominator will be a polynomial.

How to multiply and divide rational expressions?

Multiplying Rational Expressions:

When multiplying rational expressions there are 3 main steps:

1. Multiply the numerators.
2. Multiply the denominators.
3. Rewrite as a rational expression and simplify when possible.

Let’s look at an example:

In the example, below, we will first multiply the numerators

The numerators are 5x and 2x.

(5x)(2x)= 10x².

Next multiply the denominators.

The denominators are 3 and 7.

3x7=21.

Now rewrite this as a rational expression.

Our product will be:

This can not be simplified any further, so this is the final answer.

Dividing Rational Expressions:

When dividing rational expressions there are 4 main steps:

1. Multiply the first expression times the reciprocal of the second expression (Just like dividing fractions).
2. Multiply the numerators.
3. Multiply the denominators.
4. Rewrite as a rational expression and simplify when possible.

Let’s look at an example:

In the example, below, we will first multiply the first expression times the reciprocal of the second expression:

When we rewrite with the reciprocal it becomes:

Now we need to multiply the numerators. The numerators are 5 and 1.

(5)(1)= 5

Next multiply the denominators.

The denominators are (x+3) and (x+3).

(x+3)(x+3)= x²+3x+3x+9= x²+6x+9

Now rewrite this as a rational expression.

Our quotient will be:

This can not be simplified any further.