I am trying to help my daughter with this problem

2+square root of 5 over 3 - square root of 6. Please come to my rescue!

2. have your daughter multiply numerator and denominator by

$\displaystyle 3 + \sqrt{6}$

then simplify.

3. Not 3-square root of 6?

4. Originally Posted by mommyneedshelp
I am trying to help my daughter with this problem

2+square root of 5 over 3 - square root of 6. Please come to my rescue!
In a fraction, you do not keep a surd ($\displaystyle \sqrt{x}$) on the denominator so when it says to simplify the expression, your aim is to remove the surd from the denominator.

$\displaystyle \frac{2+\sqrt{5}}{3-\sqrt{6}}$

Multiply the numerator and the denominator by the conjugate of the denominator which is $\displaystyle 3+\sqrt{6}$

$\displaystyle \left(\frac{2+\sqrt{5}}{3-\sqrt{6}}\right)\left(\frac{3+\sqrt{6}}{3+\sqrt{6} }\right)$

Multiply all the expressions. Numerator with numerator and denominator with denominator.

$\displaystyle =\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{9 + 3\sqrt{6} - 3\sqrt{6} -6}$

$\displaystyle =\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{3}$

5. Thank you so much for your help!