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:

 

a3	÷	7a2
10		5

 

Answer

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

 

a3	x	5
10		7a2

 

Now multiply the numerators to get 5a³

And multiply the denominators to get 70a²

 

This gives us:

 

5a3

70a2

 

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

 

a

14

 

Let's try some questions.