How do you differentiate f(x)=(3x)/(x-2)-6/(x-2) using the quotient rule?

Jun 7, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

Explanation:

Given -

$y = \frac{3 x}{x - 2} - \frac{6}{x - 2}$

Since $x - 2$ is common to both fractions

$y = \frac{3 x - 6}{x - 2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left[\left(x - 2\right) \left(3\right)\right] - \left[\left(3 x - 6\right) \left(1\right)\right]}{x - 2} ^ 2$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left[3 x - 6\right] - \left[3 x - 6\right]}{x - 2} ^ 2$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 x - 6 - 3 x + 6}{x - 2} ^ 2$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{0}{x - 2} ^ 2 = 0$