Rationalize the Denominator
(√a-√b)/(√a+√b)
I have literally no idea how to do this one. It's an online class so I have no teacher to ask at the moment and need help. Also i copy and pasted the square root symbols, just to let you know.
Hey! multiply both the numerator and denominator by the conjugate. in this case it's square root a - square root b.
To rationalize the denominator of the given expression (√a-√b)/(√a+√b), you can use the conjugate method.
The conjugate of a binomial expression (√a+√b) is obtained by changing the sign between the terms, so the conjugate of (√a+√b) is (√a-√b). To rationalize the denominator, multiply both the numerator and the denominator of the expression by the conjugate of the denominator.
(√a-√b)/(√a+√b) * (√a-√b)/(√a-√b)
Now, let's simplify the expression:
Numerator: (√a - √b) * (√a - √b) = (√a)^2 - 2√a√b + (√b)^2 = a - 2√ab + b
Denominator: (√a + √b) * (√a - √b) = (√a)^2 - (√b)^2 = a - b
The fully simplified expression is (a - 2√ab + b)/(a - b).
So, the rationalized form of (√a-√b)/(√a+√b) is (a - 2√ab + b)/(a - b).