How Did Correcting a Simple Algebra Error Lead to the Right Solution?

[Savipats]

Homework Statement

Homework Equations

a^2-b^2 = (a+b)(a-b)
a^2-2ab+b^2 = (a-b)(a-b)
a^2+2ab+b^2 = (a+b)(a+b)

The Attempt at a Solution

SOLVED IT! Look at the bottom!

With my first try i got the answer 0
The result of first parenthesis was 1 /(√x+√y)

From there on it went like this 1 /(√x+√y) - 1 /(√x+√y) = 0

I'm suspecting that i might have messed up the order of operations, but not sure. I did the calculation inside the paranthesis first, then reversed it (^-1)

The answer should come like this
(2√y)/(x-y)

Solution:
Should be more careful next time.. i made an error when writing it down for myself. :) Now, with the correct signs i got

1 /(√x-√y) from the first paranthesis, and from there on it was all piece of cake. Thanks.

 

[nate808]

it is important to be thorough and precise in your calculations. It is possible that you may have made a mistake in your order of operations or in your substitution of variables. It is always a good idea to double check your work and make sure that all steps are correct before moving on to the next step. In this case, it seems like you were able to identify and correct your mistake, which is a great problem-solving skill to have in science. Keep up the good work!