Rationalize the denominator, assume that all expressions under radicals represent postive numbers.
sqrt:a - sqrt:b/sqrt:a + sqrt:b
(a-2sqrt:ab+b)/(a-b)
To rationalize the denominator of the given expression, we need to eliminate any square roots from the denominator. In this case, we have a binomial expression in the denominator, specifically √a + √b.
To eliminate the square root, we can multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a binomial expression of the form √x + √y is √x - √y.
So, let's multiply the numerator and denominator by the conjugate of the denominator (√a - √b):
[ √a - √b / √a + √b ] * [ (√a - √b) / (√a - √b) ]
Expanding the numerator and the denominator:
[ ( √a * √a ) - ( √a * √b ) - ( √b * √a ) - ( √b * √b ) ] / ( √a * √a ) - ( √a * √b ) + ( √a * √b ) - ( √b * √b )
Simplifying the expression:
[ a - √ab - √ab - b ] / ( a - b )
Combining like terms:
[ a - 2√ab - b ] / ( a - b )
So, the rationalized form of the given expression is:
( a - 2√ab - b ) / ( a - b )