Solve 21-z^-1/1+z^-1+4

$$2 \frac{ 1- { z }^{ -1 } }{ 1+ { z }^{ -1 } } +4$$

Evaluate

$$\frac{2\left(3z+1\right)}{z+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-z^{-1}}{1+z^{-1}}.

$$2\times \frac{\frac{1}{z}\left(z-1\right)}{\frac{1}{z}\left(z+1\right)}+4$$

Cancel out \frac{1}{z} in both numerator and denominator.

$$2\times \frac{z-1}{z+1}+4$$

Express 2\times \frac{z-1}{z+1} as a single fraction.

$$\frac{2\left(z-1\right)}{z+1}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z+1}{z+1}.

$$\frac{2\left(z-1\right)}{z+1}+\frac{4\left(z+1\right)}{z+1}$$

Since \frac{2\left(z-1\right)}{z+1} and \frac{4\left(z+1\right)}{z+1} have the same denominator, add them by adding their numerators.

$$\frac{2\left(z-1\right)+4\left(z+1\right)}{z+1}$$

Do the multiplications in 2\left(z-1\right)+4\left(z+1\right).

$$\frac{2z-2+4z+4}{z+1}$$

Combine like terms in 2z-2+4z+4.

$$\frac{6z+2}{z+1}$$

Expand

$$\frac{2\left(3z+1\right)}{z+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-z^{-1}}{1+z^{-1}}.

$$2\times \frac{\frac{1}{z}\left(z-1\right)}{\frac{1}{z}\left(z+1\right)}+4$$

Cancel out \frac{1}{z} in both numerator and denominator.

$$2\times \frac{z-1}{z+1}+4$$

Express 2\times \frac{z-1}{z+1} as a single fraction.

$$\frac{2\left(z-1\right)}{z+1}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z+1}{z+1}.

$$\frac{2\left(z-1\right)}{z+1}+\frac{4\left(z+1\right)}{z+1}$$

Since \frac{2\left(z-1\right)}{z+1} and \frac{4\left(z+1\right)}{z+1} have the same denominator, add them by adding their numerators.

$$\frac{2\left(z-1\right)+4\left(z+1\right)}{z+1}$$

Do the multiplications in 2\left(z-1\right)+4\left(z+1\right).

$$\frac{2z-2+4z+4}{z+1}$$

Combine like terms in 2z-2+4z+4.

$$\frac{6z+2}{z+1}$$