# How do you simplify and state the excluded values for (3x) /( 1-3x)?

Jul 27, 2015

I am afraid there is not much to simplify.

#### Explanation:

The excluded value for $x$ is when $1 - 3 x = 0 \implies x \ne \frac{1}{3}$

because you may not divide by $0$.

Jul 27, 2015

Excluded value : $x = \frac{1}{3}$

#### Explanation:

Add and subtract $\left(1\right)$ from the numerator to get from $\text{ "(3x)/(1-3x)" }$ to this : $\frac{1 + 3 x - 1}{1 - 3 x} \text{ }$

then to " "(3x-1)/(1-3x) +1/(1-3x)

Which could also be written as : $\frac{- 1 \cdot \left(3 x - 1\right)}{\left(3 x - 1\right)} + \frac{1}{1 - 3 x} \textcolor{red}{=} \textcolor{b l u e}{\frac{1}{1 - 3 x} - 1}$

Now, we can see that if $\left(1 - 3 x\right) = 0$ the expression would be undefined in $\mathbb{R}$

So, we say that the excluded values of $x$ are those for which $\left(1 - 3 x\right) = 0$

$\implies 3 x = 1 \implies \textcolor{b l u e}{x = \frac{1}{3}} \text{ }$ is the excluded value.