Y^-1 - x^-1 / x^-1 - y^-1

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вопрос

To simplify the expression Y^-1 - x^-1 / x^-1 - y^-1, we can find a common denominator and combine the terms.

First, find a common denominator for the fractions:

Y^-1 = 1/Y
x^-1 = 1/x

So, the expression becomes:

(1/Y - 1/x) / (1/x - 1/Y)

To combine the fractions in the numerator, we need to find a common denominator. The common denominator in this case is Y*x:

1/Y = x/(Yx)
1/x = Y/(Yx)

Thus, the expression becomes:

(x/(Yx) - Y/(Yx)) / (Y/(Yx) - x/(Yx))

Now, simplify the expression further:

[(x - Y)/(Yx)] / [(Y - x)/(Yx)]

Since we are dividing fractions, we can multiply by the reciprocal of the second fraction:

[(x - Y)/(Yx)] [(Y*x)/(Y - x)]

This simplifies to:

(x - Y) / (Y - x)

Therefore, Y^-1 - x^-1 / x^-1 - y^-1 simplifies to (x - Y) / (Y - x) when all terms are in fraction form.