I chose this because its important to understand the rules to be able to complete the operations correctly.

Dividing monomials is pretty simple, as you simply divide as you think you would divide, so in this post I will focus on dividing binomials, which includes using a conjugate.

What is a conjugate? The conjugate of 1+2 is 1-2, so it’s simply just switching the sign in the middle of an operation.

First, we need the conjugate of the denominator to cancel it out, as we can see the conjugate of is

Next, we multiple the nominator and denominator by the conjugate to cancel out the denominator.

So:

Now we need to properly distribute by multiplying as usual.

is also the same as

This can still be further simplified by multiplying top and bottom by -1, which will reverse the signs.

After that, we still need to distribute in the nominator, giving us:

is also the same as which is the same as