Solve 1/z-1=2/z+1

$$\frac{ 1 }{ z-1 } = \frac{ 2 }{ z+1 }$$

Solve for z

$$z=3$$

Steps for Solving Linear Equation

Variable z cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(z-1\right)\left(z+1\right), the least common multiple of z-1,z+1.

$$z+1=\left(z-1\right)\times 2$$

Use the distributive property to multiply z-1 by 2.

$$z+1=2z-2$$

Subtract 2z from both sides.

$$z+1-2z=-2$$

Combine z and -2z to get -z.

$$-z+1=-2$$

Subtract 1 from both sides.

$$-z=-2-1$$

Subtract 1 from -2 to get -3.

$$-z=-3$$

Multiply both sides by -1.

$$z=3$$