## anonymous one year ago I need step by step detail on how to solve this problem.

1. anonymous

$\frac{ \sqrt{a }+2\sqrt{y} }{ \sqrt{a}-2\sqrt{y} }$ Rationalize the denominator and simplify.

2. DanJS

$\frac{ \sqrt{a}+2\sqrt{y} }{ \sqrt{a}+2\sqrt{y}}$

3. DanJS

multiply by that

4. anonymous

$\frac{ (\sqrt{a}+2\sqrt{y})^{2} }{ (\sqrt{a})^{2}-(2\sqrt{y})^{2} }$ That's really as far as I can take it because it's the actual multiplying radicals and simplifying stuff that I have trouble with.

5. DanJS

The numerator expands to $(\sqrt{a}+2\sqrt{y})^2 = \sqrt{a}^2+4\sqrt{a}\sqrt{y}+4\sqrt{y}^2 = a + 4\sqrt{a}\sqrt{y}+4y$

6. DanJS

denominator goes to $a - 4y$

7. DanJS

no more roots in denominator, which is what they want

8. anonymous

Ohhh Ok so that was what I kept getting but in the denominator I mixed it up and got it a+4y so that was my problem. Thank you that makes a lot more sense.

9. DanJS

welcome, goodluck