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Simplify (x-y/√x-√y)-√x

User Volcanic
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Negative square root of y is the answer
User Takachi
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To simplify the expression, we can first rationalize the denominator of the fraction by multiplying both the numerator and denominator by the conjugate of the denominator, which is (√x + √y):


(x - y/√x - √y) = (x - y/√x - √y) * (√x + √y)/(√x + √y)
= [(x - y) (√x + √y)] / [(√x - √y)(√x + √y)]
= (x√x - xy + xy - y√y) / (x - y)
= (√x - √y)
So the expression simplifies to:

(x - y/√x - √y) - √x = (√x - √y) - √x
= -√y
Therefore, the simplified expression is -√y.
User Roadies
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