Find the x and y Intercepts y=(2x)/(x-1)

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

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{2 x}{x - 1}$

Solve the equation.

Set the numerator equal to zero.

$2 x = 0$

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

x-intercept(s) in point form.

x-intercept(s): $(0, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{2 (0)}{(0) - 1}$

Solve the equation.

Remove parentheses.

$y = \frac{2 (0)}{0 - 1}$

Remove parentheses.

$y = \frac{2 (0)}{(0) - 1}$

Simplify $\frac{2 (0)}{(0) - 1}$ .

Multiply $2$ by $0$ .

$y = \frac{0}{0 - 1}$

Subtract $1$ from $0$ .

$y = \frac{0}{- 1}$

Divide $0$ by $- 1$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(0, 0)$

y-intercept(s): $(0, 0)$

Step 4