Question

I need help this is due at 11:59 tonight!

Answer 1

Answer:

$\frac{1-4\sqrt{6}}{5}$

Step-by-step explanation:

$\frac{\sqrt{6}-5}{\sqrt{6}-1}$

In order to rationalize the denominator, you must multiply the top and bottom by the bottom's conjugate. The conjugate of $\sqrt{6}-1$ is $\sqrt{6}+1$. The reason we do this is because when you multiply conjugates, all you have to do is multiply first terms and last terms (of the foil method).

So we are doing:

$\frac{\sqrt{6}-5}{\sqrt{6}-1} \cdot \frac{\sqrt{6}+1}{\sqrt{6}+1}$

You will have to use the full foil method on top:

$\frac{6+\sqrt{6}-5\sqrt{6}-5}{6-1}$

Reorder top using commutative property to put "like terms" together:

$\frac{6-5+\sqrt{6}-5\sqrt{6}}{5}$

Simplify:

$\frac{1-4\sqrt{6}}{5}$