( \frac{x}{x-1}-1 ) * \frac{xy-y}{x}

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вопрос

To simplify the given expression:

( \frac{x}{x-1}-1 ) * \frac{xy-y}{x}

First, let's simplify the expression within the parentheses:

\frac{x}{x-1} - 1

To combine the fractions, you need a common denominator. The common denominator would be (x-1):

\frac{x}{x-1} - \frac{x-1}{x-1}

\frac{x - (x-1)}{x-1}

\frac{x - x + 1}{x-1}

\frac{1}{x-1}

Now substituting this back into the original expression:

( \frac{1}{x-1} ) * \frac{xy-y}{x}

Now multiply the fractions:

( \frac{1}{x-1} ) * \frac{xy-y}{x}

\frac{xy-y}{x(x-1)}

Therefore, the simplified expression is \frac{xy-y}{x(x-1)}.