Solve a+1/a+1/a-a

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

Evaluate

$$\frac{2}{a}$$

Solution Steps

Combine \frac{1}{a} and \frac{1}{a} to get 2\times \frac{1}{a}.

$$a+2\times \frac{1}{a}-a$$

Combine a and -a to get 0.

$$2\times \frac{1}{a}$$

Express 2\times \frac{1}{a} as a single fraction.

$$\frac{2}{a}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

Combine \frac{1}{a} and \frac{1}{a} to get 2\times \frac{1}{a}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a+2\times \frac{1}{a}-a)$$

Combine a and -a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2\times \frac{1}{a})$$

Express 2\times \frac{1}{a} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{a})$$

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

$$-2a^{-1-1}$$

Subtract 1 from -1.

$$-2a^{-2}$$