Solve f(x)=ax-a/x-1

$$f ( x ) = \frac { a x - a } { x - 1 }$$

Evaluate

$$a$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{a\left(x-1\right)}{x-1}$$

Cancel out x-1 in both numerator and denominator.

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{ax-a}{x-1}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a\left(x-1\right)}{x-1})$$

Cancel out x-1 in both numerator and denominator.

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

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

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

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

$$1$$