Solve (1*frac{e^{1}+e^{-1}}{2}-e^1-e^-1/2)-(0-e^0-e^-0/2)

$$( 1 \cdot \frac { e ^ { 1 } + e ^ { - 1 } } { 2 } - \frac { e ^ { 1 } - e ^ { - 1 } } { 2 } ) - ( 0 - \frac { e ^ { 0 } - e ^ { - 0 } } { 2 } )$$

Evaluate

$$\frac{1}{e}\approx 0.367879441$$

Short Solution Steps

Calculate e to the power of 1 and get e.

$$1\times \frac{e+e^{-1}}{2}-\frac{e^{1}-e^{-1}}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

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

$$\frac{e+e^{-1}}{2}-\frac{e^{1}-e^{-1}}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Calculate e to the power of 1 and get e.

$$\frac{e+e^{-1}}{2}-\frac{e-e^{-1}}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Since \frac{e+e^{-1}}{2} and \frac{e-e^{-1}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{e+e^{-1}-\left(e-e^{-1}\right)}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Do the multiplications in e+e^{-1}-\left(e-e^{-1}\right).

$$\frac{e+\frac{1}{e}-e+\frac{1}{e}}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Combine like terms in e+\frac{1}{e}-e+\frac{1}{e}.

$$\frac{2\times \frac{1}{e}}{2}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Cancel out 2 and 2.

$$\frac{1}{e}-\left(0-\frac{e^{0}-e^{0}}{2}\right)$$

Calculate e to the power of 0 and get 1.

$$\frac{1}{e}-\left(0-\frac{1-e^{0}}{2}\right)$$

Calculate e to the power of 0 and get 1.

$$\frac{1}{e}-\left(0-\frac{1-1}{2}\right)$$

Subtract 1 from 1 to get 0.

$$\frac{1}{e}-\left(0-\frac{0}{2}\right)$$

Zero divided by any non-zero number gives zero.

$$\frac{1}{e}-\left(0+0\right)$$

Add 0 and 0 to get 0.

$$\frac{1}{e}-0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 0 times \frac{e}{e}.

$$\frac{1}{e}-\frac{0e}{e}$$

Since \frac{1}{e} and \frac{0e}{e} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-0e}{e}$$

Do the multiplications in 1-0e.

$$\frac{1}{e}$$