How do you differentiate g(x)=(3-1/x)/(x+5) using the quotient rule?

May 16, 2017

I would change the form first.

Explanation:

Multiply by $\frac{x}{x}$ to get

$g \left(x\right) = \frac{3 x - 1}{{x}^{2} + 5 x}$

So,

$g ' \left(x\right) = \frac{\left(3\right) \left({x}^{2} + 5 x\right) - \left(3 x - 1\right) \left(2 x + 5\right)}{{x}^{2} + 5 x} ^ 2$

$= \frac{3 {x}^{2} + 15 x - 6 {x}^{2} - 15 x + 2 x + 5}{{x}^{2} + 5 x} ^ 2$

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