sqrt r - sqrt s/ sqrt r + sqrt s =r sqrt r- sqrt rs +sqrt s/ r
Can see if I did this right.
To verify if you simplified the expression correctly, let's go step by step.
The given expression is:
(sqrt(r) - sqrt(s)) / (sqrt(r) + sqrt(s))
To simplify this expression, we need to rationalize the denominator. To do that, we will multiply both the numerator and the denominator by the conjugate of the denominator, which is (sqrt(r) - sqrt(s)).
= [(sqrt(r) - sqrt(s)) / (sqrt(r) + sqrt(s))] * [(sqrt(r) - sqrt(s)) / (sqrt(r) - sqrt(s))]
Multiplying the numerators and the denominators together gives us:
= (sqrt(r) - sqrt(s))^2 / [(sqrt(r))^2 - (sqrt(s))^2]
Using the formula (a - b)^2 = a^2 - 2ab + b^2 in the numerator, and simplifying in the denominator, we get:
= (r - 2sqrt(rs) + s) / (r - s)
Therefore, the simplified expression is:
(r - 2sqrt(rs) + s) / (r - s)
Now, let's compare it to the expression you provided:
r sqrt(r) - sqrt(rs) + sqrt(s) / r
These two expressions are not equivalent. So, it seems that there might be an error in your simplification. Double-check your steps and calculations to find the mistake.