Solve 3/21/z+1+1/21/z-1

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

Evaluate

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

Short Solution Steps

Multiply \frac{3}{2} times \frac{1}{z+1} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \frac{1}{2} times \frac{1}{z-1} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(z+1\right) and 2\left(z-1\right) is 2\left(z-1\right)\left(z+1\right). Multiply \frac{3}{2\left(z+1\right)} times \frac{z-1}{z-1}. Multiply \frac{1}{2\left(z-1\right)} times \frac{z+1}{z+1}.

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

Since \frac{3\left(z-1\right)}{2\left(z-1\right)\left(z+1\right)} and \frac{z+1}{2\left(z-1\right)\left(z+1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(z-1\right)+z+1.

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

Combine like terms in 3z-3+z+1.

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

Factor the expressions that are not already factored in \frac{4z-2}{2\left(z-1\right)\left(z+1\right)}.

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

Cancel out 2 in both numerator and denominator.

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

Expand \left(z-1\right)\left(z+1\right).

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

Factor

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