Solving for X involving Square Roots

[yoyo]

Hi, I am getting frustrated with trying to solve this equation:

sqrt(x+9) - sqrt(x-6) = 3.

I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help. Thanks in advance.

 

[Diffy]

Can you show how squaring both sides cancels out the x?

If I square both sides I get:

(sqrt(x+9) - sqrt (x-6))^2 = 3^2

x+9 - 2*sqrt(x+9)*sqrt(x-6) + x - 6 = 9

2x + 3 - 2*sqrt((x+9)(x-6)) = 9
...

 

[yoyo]

oh i see what you are saying. Silly mistake on me. Thank you so much!