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Verified answer
(x^(-1) - y^(-1))/(x^(1/2) + y^(1/2))= (1/x - 1/y)/(√x + √y)
= ((y - x)/xy)/(√x + √y)
= (y - x)/[ (xy)(√x + √y) ]
= (√x + √y)(-√x + √y)/[ (xy)(√x + √y) ]
= (-√x + √y)/(xy)
= (√y - √x)/xy