Solve 2/n-5div6a/3n-15

$$\frac { 2 } { n - 5 } \div \frac { 6 a } { 3 n - 15 }$$

Evaluate

$$\frac{1}{a}$$

Short Solution Steps

Divide \frac{2}{n-5} by \frac{6a}{3n-15} by multiplying \frac{2}{n-5} by the reciprocal of \frac{6a}{3n-15}.

$$\frac{2\left(3n-15\right)}{\left(n-5\right)\times 6a}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3n-15}{3a\left(n-5\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(n-5\right)}{3a\left(n-5\right)}$$

Cancel out 3\left(n-5\right) in both numerator and denominator.

$$\frac{1}{a}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

Divide \frac{2}{n-5} by \frac{6a}{3n-15} by multiplying \frac{2}{n-5} by the reciprocal of \frac{6a}{3n-15}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\left(3n-15\right)}{\left(n-5\right)\times 6a})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3n-15}{3a\left(n-5\right)})$$

Factor the expressions that are not already factored in \frac{3n-15}{3a\left(n-5\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3\left(n-5\right)}{3a\left(n-5\right)})$$

Cancel out 3\left(n-5\right) in both numerator and denominator.

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

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

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

Subtract 1 from -1.

$$-a^{-2}$$