# If f(x) = 3x-6 and g(x) = x-2, what is f/g and its domain?

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Aug 20, 2017

See a solution process below:

#### Explanation:

We can write $\left(\frac{f}{g}\right) \left(x\right)$ as:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{3 x - 6}{x - 2}$

Factoring the numerator gives:

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

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

$\left(\frac{f}{g}\right) \left(x\right) = \frac{3 \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 2\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 2}}}}$

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

The domain of this function is all Real numbers where $\left(x - 2\right) \ne 0$ or where $x \ne 2$

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