Solve 2/1-z=3/1+z

$$\frac { 2 } { 1 - z } = \frac { 3 } { 1 + z }$$

Solve for z

$$z=\frac{1}{5}=0.2$$

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 1-z,1+z.

$$-\left(1+z\right)\times 2=\left(z-1\right)\times 3$$

To find the opposite of 1+z, find the opposite of each term.

$$\left(-1-z\right)\times 2=\left(z-1\right)\times 3$$

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

$$-2-2z=\left(z-1\right)\times 3$$

Use the distributive property to multiply z-1 by 3.

$$-2-2z=3z-3$$

Subtract 3z from both sides.

$$-2-2z-3z=-3$$

Combine -2z and -3z to get -5z.

$$-2-5z=-3$$

Add 2 to both sides.

$$-5z=-3+2$$

Add -3 and 2 to get -1.

$$-5z=-1$$

Divide both sides by -5.

$$z=\frac{-1}{-5}$$

Fraction \frac{-1}{-5} can be simplified to \frac{1}{5} by removing the negative sign from both the numerator and the denominator.

$$z=\frac{1}{5}$$