# f(x)=3x-1 and g(x)=x-2. How do you solve (f/g)(x)?

Oct 23, 2017

$x = \frac{1}{3}$

Refer to the explanation for the process.

#### Explanation:

$f \left(x\right) = 3 x - 1$

$g \left(x\right) = x - 2$

$\left(\frac{f}{g}\right) \left(x\right)$ means to divide the expression for $f \left(x\right)$ by the expression for $g \left(x\right)$.

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

Set $\left(\frac{f}{g}\right) \left(x\right)$ equal to $0$.

$0 = \frac{3 x - 1}{x - 2}$

Multiply both sides by $\left(x - 2\right)$.

$0 \left(x - 2\right) = \frac{3 x - 1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 2\right)}}}} ^ 1 \times {\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 2\right)}}}}^{1}$

Simplify.

$0 = 3 x - 1$

Switch sides.

$3 x - 1 = 0$

Add $1$ to both sides.

$3 x = 1$

Divide both sides by $3$.

$x = \frac{1}{3}$