This week of precal we learned about division of radicals and rationalizing the denominator. It is (obviously) very helpful to rationalize the denominator in a question where the denominator isn’t a rational number. Let’s use this equation as an example:

Now, we know that the denominator is irrational. In order to solve the equation we must rationalize it and the easiest way to do that is by multiplying it by the conjugate of itself (√5+1), remembering that what you do to the bottom you must do to the top.

This is what you get from multiplying the top and bottom by the conjugate of the denominator (√5+1).

In this particular equation we can further simplify it because there is a common factor (4). we can divide the 4s on the top by the 4 on the bottom resulting in √[5+4]. And that is how you simplify a division equation that has an irrational denominator