Solve 1/frac{1{x-1}}+1

$$\frac { 1 } { \frac { 1 } { x - 1 } } + 1$$

Evaluate

$$x$$

Solution Steps

Divide 1 by \frac{1}{x-1} by multiplying 1 by the reciprocal of \frac{1}{x-1}.

$$x-1+1$$

Add -1 and 1 to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Divide 1 by \frac{1}{x-1} by multiplying 1 by the reciprocal of \frac{1}{x-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-1+1)$$

Add -1 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$