Solve for y x=(2y)/(y-1)

$x = \frac{2 y}{y - 1}$

Step 1

Multiply the equation by $y - 1$ .

$(y - 1) (x) = (\frac{2 y}{y - 1}) (y - 1)$

Step 2

Simplify the left side.

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

Apply the distributive property.

$y x - 1 x = (\frac{2 y}{y - 1}) (y - 1)$

Rewrite $- 1 x$ as $- x$ .

$y x - x = (\frac{2 y}{y - 1}) (y - 1)$

$y x - x = (\frac{2 y}{y - 1}) (y - 1)$

$y x - x = (\frac{2 y}{y - 1}) (y - 1)$

Step 3

Simplify the right side.

Cancel the common factor of $y - 1$ .

Cancel the common factor.

$y x - x = \frac{2 y}{y - 1} (y - 1)$

Rewrite the expression.

$y x - x = 2 y$

$y x - x = 2 y$

$y x - x = 2 y$

Step 4

Solve for $y$ .

Subtract $2 y$ from both sides of the equation.

$y x - x - 2 y = 0$

Add $x$ to both sides of the equation.

$y x - 2 y = x$

Factor $y$ out of $y x - 2 y$ .

Factor $y$ out of $y x$ .

$y (x) - 2 y = x$

Factor $y$ out of $- 2 y$ .

$y (x) + y \cdot - 2 = x$

Factor $y$ out of $y (x) + y \cdot - 2$ .

$y (x - 2) = x$

$y (x - 2) = x$

Divide each term in $y (x - 2) = x$ by $x - 2$ and simplify.

Divide each term in $y (x - 2) = x$ by $x - 2$ .

$\frac{y (x - 2)}{x - 2} = \frac{x}{x - 2}$

Simplify the left side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{y (x - 2)}{x - 2} = \frac{x}{x - 2}$

Divide $y$ by $1$ .

$y = \frac{x}{x - 2}$

$y = \frac{x}{x - 2}$

$y = \frac{x}{x - 2}$

$y = \frac{x}{x - 2}$

$y = \frac{x}{x - 2}$

Related Questions