Solve -1/2left(z-1right)+1/2left(z+1right)-1/2left(z-1right)^2-1/2left(z+1right)

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

Evaluate

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

Short Solution Steps

Subtract \frac{1}{2\left(z+1\right)} from \frac{1}{2\left(z+1\right)} to get 0.

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

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)^{2} is 2\left(z-1\right)^{2}. Multiply -\frac{1}{2\left(z-1\right)} times \frac{z-1}{z-1}.

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

Since -\frac{z-1}{2\left(z-1\right)^{2}} and \frac{1}{2\left(z-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in -z+1-1.

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

Expand 2\left(z-1\right)^{2}.

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

Expand

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

Short Solution Steps

Subtract \frac{1}{2\left(z+1\right)} from \frac{1}{2\left(z+1\right)} to get 0.

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

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)^{2} is 2\left(z-1\right)^{2}. Multiply -\frac{1}{2\left(z-1\right)} times \frac{z-1}{z-1}.

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

Since -\frac{z-1}{2\left(z-1\right)^{2}} and \frac{1}{2\left(z-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in -z+1-1.

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

Expand 2\left(z-1\right)^{2}.

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