Solve d^-1+e^-1/frac{d^2-e^2{de}}

$$\frac { d ^ { - 1 } + e ^ { - 1 } } { \frac { d ^ { 2 } - e ^ { 2 } } { d e } }$$

Evaluate

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

Short Solution Steps

Divide d^{-1}+e^{-1} by \frac{d^{2}-e^{2}}{de} by multiplying d^{-1}+e^{-1} by the reciprocal of \frac{d^{2}-e^{2}}{de}.

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

Use the distributive property to multiply d^{-1}+e^{-1} by d.

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

Multiply d^{-1} and d to get 1.

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

Use the distributive property to multiply 1+e^{-1}d by e.

$$\frac{e+e^{-1}de}{d^{2}-e^{2}}$$

Multiply e^{-1} and e to get 1.

$$\frac{e+d}{d^{2}-e^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out d+e in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide d^{-1}+e^{-1} by \frac{d^{2}-e^{2}}{de} by multiplying d^{-1}+e^{-1} by the reciprocal of \frac{d^{2}-e^{2}}{de}.

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

Use the distributive property to multiply d^{-1}+e^{-1} by d.

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

Multiply d^{-1} and d to get 1.

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

Use the distributive property to multiply 1+e^{-1}d by e.

$$\frac{e+e^{-1}de}{d^{2}-e^{2}}$$

Multiply e^{-1} and e to get 1.

$$\frac{e+d}{d^{2}-e^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out d+e in both numerator and denominator.

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