1. ## Radical Expressions with 2 variables

Hello. I'm just helping a friend, and it's been so long since I've had this. I don't know how to write a square root sign, so it's sqrt.

Sqrt x
------- (over)

3 Sqrt x - sqrt y

Is this as simplified as it can be? If it's possible to see the steps, or to be pointed to a resource to see the steps, I know it'll come back to me. Thank you!

2. Originally Posted by ForgottenMyMath
Hello. I'm just helping a friend, and it's been so long since I've had this. I don't know how to write a square root sign, so it's sqrt.

Sqrt x
------- (over)

3 Sqrt x - sqrt y

Is this as simplified as it can be? If it's possible to see the steps, or to be pointed to a resource to see the steps, I know it'll come back to me. Thank you!

You can rationalise

$\displaystyle \frac{\sqrt{x}}{3\sqrt{x}-\sqrt{y}} \cdot \frac{3\sqrt{x}+\sqrt{y}}{3\sqrt{x}+\sqrt{y}}$

$\displaystyle \frac{3x+\sqrt{xy}}{(3\sqrt{x})^2-(\sqrt{y})^2}$

$\displaystyle \frac{3x+\sqrt{xy}}{9x-y}$

3. Thank you!