Solve x/x-2=e

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

Solve for x

$$x=-\frac{2e}{1-e}\approx 3.163953414$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$x=e\left(x-2\right)$$

Use the distributive property to multiply e by x-2.

$$x=ex-2e$$

Subtract ex from both sides.

$$x-ex=-2e$$

Reorder the terms.

$$-ex+x=-2e$$

Combine all terms containing x.

$$\left(-e+1\right)x=-2e$$

The equation is in standard form.

$$\left(1-e\right)x=-2e$$

Divide both sides by -e+1.

$$\frac{\left(1-e\right)x}{1-e}=-\frac{2e}{1-e}$$

Dividing by -e+1 undoes the multiplication by -e+1.

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

Variable x cannot be equal to 2.

$$x=-\frac{2e}{1-e}\text{, }x\neq 2$$