Solve a-1/adiva-1/a^2

$$\frac { a - 1 } { a } \div \frac { a - 1 } { a ^ { 2 } }$$

Evaluate

$$a$$

Solution Steps

Divide \frac{a-1}{a} by \frac{a-1}{a^{2}} by multiplying \frac{a-1}{a} by the reciprocal of \frac{a-1}{a^{2}}.

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

Cancel out a\left(a-1\right) in both numerator and denominator.

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

Divide \frac{a-1}{a} by \frac{a-1}{a^{2}} by multiplying \frac{a-1}{a} by the reciprocal of \frac{a-1}{a^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\left(a-1\right)a^{2}}{a\left(a-1\right)})$$

Cancel out a\left(a-1\right) 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.

$$1$$