hi i had this problem on my test and did not find any way to solve it but im verry intressted how to solve it! plz any1 can help:O?
Write the expression of the form , where K and L are rational numbers.
You want to multiply the expression by 1 in the form of the conjugate of the denominator over itself, i.e.:
$\displaystyle \frac{5\sqrt{2}-2\sqrt{3}}{5\sqrt{2}+2\sqrt{3}}\cdot\frac{5\sqrt{2 }-2\sqrt{3}}{5\sqrt{2}-2\sqrt{3}}$
Now, perform the multiplication...
$\displaystyle \frac{5\sqrt{2}-2\sqrt{3}}{5\sqrt{2}+2\sqrt{3}}\cdot\frac{5\sqrt{2 }-2\sqrt{3}}{5\sqrt{2}-2\sqrt{3}}=$
$\displaystyle \frac{5^2\cdot2-2\cdot2\cdot5\cdot\sqrt{2}\cdot\sqrt{3}+2^2\cdot3} {5^2\cdot2-2^2\cdot3}=$
$\displaystyle \frac{50-20\sqrt{6}+12}{50-12}$
Can you finish?
As far as using $\displaystyle \LaTeX$, there are tutorials here and online that will do a much better job of explaining its usage than I can do in a single post.