# How do you simplify and find the excluded value of (m - 3 )/( 3 - m )?

May 19, 2017

See a solution process below:

#### Explanation:

First, rewrite the numerator as:

$\frac{- 1 \left(- m + 3\right)}{3 - m} \implies \frac{- 1 \left(3 - m\right)}{3 - m}$

Now, cancel like terms in the numerator and denominator to complete the simplification:

$\frac{- 1 \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(3 - m\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3 - m}}}} \implies - 1$

Because we cannot divide by $0$ the numerator, or, $3 - m$ cannot equal $0$.

To find the excluded value set $3 - m$ equal to $0$ and solve for $m$:

$3 - m = 0$

$- \textcolor{red}{3} + 3 - m = - \textcolor{red}{3} + 0$

$0 - m = - 3$

$- m = - 3$

$\textcolor{red}{- 1} \times - m = \textcolor{red}{- 1} \times - 3$

$m = 3$

The excluded value is $m = 3$