# How do you differentiate f(x)= (2 x^2 - x - 6 )/ (x- 1 ) using the quotient rule?

##### 1 Answer
Dec 29, 2017

$f ' \left(x\right) = \frac{2 {x}^{2} - 4 x + 7}{x - 1} ^ 2$

#### Explanation:

$\text{given "f(x)=(g(x))/(h(x))" then}$

$f ' \left(x\right) = \frac{h \left(x\right) g ' \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2 \leftarrow \textcolor{b l u e}{\text{quotient rule}}$

$g \left(x\right) = 2 {x}^{2} - x - 6 \Rightarrow g ' \left(x\right) = 4 x - 1$

$h \left(x\right) = x - 1 \Rightarrow h \left(x\right) = 1$

$\Rightarrow f ' \left(x\right) = \frac{\left(x - 1\right) \left(4 x - 1\right) - \left(2 {x}^{2} - x - 6\right)}{x - 1} ^ 2$

$\textcolor{w h i t e}{\Rightarrow f ' \left(x\right)} = \frac{2 {x}^{2} - 4 x + 7}{x - 1} ^ 2$