Divide Algebraic Fractions

When we divide algebraic fractions, we use the same method as when we divide numerical fractions. 

Remember the KFC rule: Keep the first fraction, flip the second fraction and change the sign.

First, we invert the second fraction and then turn the ÷ sign into a x sign.

Then we try to reduce or cancel down any top term with a bottom term that has a common factor.

Example

Simplify:

Answer

Invert the second fraction and change the ÷ sign to a x sign.

Now multiply the numerators to get 5a³

And multiply the denominators to get 70a²

This gives us:

Now we simplify this by dividing the numbers by a common factor.

5 is a common factor of 5 and 70, so divide them both by 5. This gives us 1 as the numerator and 14 as the denominator.

Remember the rule for dividing by powers? a³ ÷ a² = a^3-2 = a

We end up with

Let's try some questions.