Solve 3/x^2-5/frac{x{x^2-5}}=

$$\frac { \frac { 3 } { x ^ { 2 } - 5 } } { \frac { x } { x ^ { 2 } - 5 } } =$$

Evaluate

$$\frac{3}{x}$$

Solution Steps

Divide \frac{3}{x^{2}-5} by \frac{x}{x^{2}-5} by multiplying \frac{3}{x^{2}-5} by the reciprocal of \frac{x}{x^{2}-5}.

$$\frac{3\left(x^{2}-5\right)}{\left(x^{2}-5\right)x}$$

Cancel out x^{2}-5 in both numerator and denominator.

$$\frac{3}{x}$$

Differentiate w.r.t. x

$$-\frac{3}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{3}{x^{2}-5} by \frac{x}{x^{2}-5} by multiplying \frac{3}{x^{2}-5} by the reciprocal of \frac{x}{x^{2}-5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x^{2}-5\right)}{\left(x^{2}-5\right)x})$$

Cancel out x^{2}-5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{x})$$

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

$$-3x^{-1-1}$$

Subtract 1 from -1.

$$-3x^{-2}$$