(1/y-1√y+1/√y-1):(√y+1/y-2√y+1) Rút gọn

To simplify the expression, we can start by finding a common denominator for the two fractions in the numerator and the denominator.

The common denominator for the numerator is y, and the common denominator for the denominator is (y-1)(y+1).

So, the expression becomes:

[(1/y - 1/√y)(√y + 1)] / [(√y + 1)(y - 2√y + 1)]

Next, we can simplify the numerator by multiplying the two fractions:

[(√y + 1 - y) / (y√y)] / [(√y + 1)(y - 2√y + 1)]

Now, let's simplify the denominator by multiplying the two binomials:

(y - 2√y + 1)(√y + 1) = y√y + y - 2y - 2√y + √y + 1 = y√y - √y - y - 1

Substituting this back into the expression, we have:

[(√y + 1 - y) / (y√y)] / [y√y - √y - y - 1]

Now, let's simplify the numerator further:

(√y + 1 - y) = √y + 1 - y

Finally, we can rewrite the expression as:

(√y + 1 - y) / (y√y - √y - y - 1)

This is the simplified form of the expression.