Solve 7/x-3/frac{x{x-3}}

$$\frac { \frac { 7 } { x - 3 } } { \frac { x } { x - 3 } }$$

Evaluate

$$\frac{7}{x}$$

Solution Steps

Divide \frac{7}{x-3} by \frac{x}{x-3} by multiplying \frac{7}{x-3} by the reciprocal of \frac{x}{x-3}.

$$\frac{7\left(x-3\right)}{\left(x-3\right)x}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{7}{x}$$

Differentiate w.r.t. x

$$-\frac{7}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{7}{x-3} by \frac{x}{x-3} by multiplying \frac{7}{x-3} by the reciprocal of \frac{x}{x-3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\left(x-3\right)}{\left(x-3\right)x})$$

Cancel out x-3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{x})$$

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

$$-7x^{-1-1}$$

Subtract 1 from -1.

$$-7x^{-2}$$