Solve for x y=x/(x-1)

$y = \frac{x}{x - 1}$

Step 1

Multiply the equation by $x - 1$ .

$(x - 1) (y) = (\frac{x}{x - 1}) (x - 1)$

Step 2

Simplify the left side.

Simplify $(x - 1) (y)$ .

Apply the distributive property.

$x y - 1 y = (\frac{x}{x - 1}) (x - 1)$

Rewrite $- 1 y$ as $- y$ .

$x y - y = (\frac{x}{x - 1}) (x - 1)$

$x y - y = (\frac{x}{x - 1}) (x - 1)$

$x y - y = (\frac{x}{x - 1}) (x - 1)$

Step 3

Simplify the right side.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$x y - y = \frac{x}{x - 1} (x - 1)$

Rewrite the expression.

$x y - y = x$

$x y - y = x$

$x y - y = x$

Step 4

Solve for $x$ .

Subtract $x$ from both sides of the equation.

$x y - y - x = 0$

Add $y$ to both sides of the equation.

$x y - x = y$

Factor $x$ out of $x y - x$ .

Factor $x$ out of $x y$ .

$x (y) - x = y$

Factor $x$ out of $- x$ .

$x (y) + x \cdot - 1 = y$

Factor $x$ out of $x (y) + x \cdot - 1$ .

$x (y - 1) = y$

$x (y - 1) = y$

Divide each term in $x (y - 1) = y$ by $y - 1$ and simplify.

Divide each term in $x (y - 1) = y$ by $y - 1$ .

$\frac{x (y - 1)}{y - 1} = \frac{y}{y - 1}$

Simplify the left side.

Cancel the common factor of $y - 1$ .

Cancel the common factor.

$\frac{x (y - 1)}{y - 1} = \frac{y}{y - 1}$

Divide $x$ by $1$ .

$x = \frac{y}{y - 1}$

$x = \frac{y}{y - 1}$

$x = \frac{y}{y - 1}$

$x = \frac{y}{y - 1}$

$x = \frac{y}{y - 1}$

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