Questions: Math 3 Question 5.5.1.5 Simplify the following expression. State any excluded values. 8m - 24 3 - m The simplified form is □, where x ≠ □. (Use a comma to separate answers as needed.)

Solution Steps

To simplify the expression \(\frac{8m - 24}{3 - m}\), we first factor the numerator and the denominator if possible. Then, we look for common factors that can be canceled out. Finally, we determine any values of \(m\) that would make the denominator zero, as these are the excluded values.

We start with the expression

\[ \frac{8m - 24}{3 - m}. \]

First, we factor the numerator:

\[ 8m - 24 = 8(m - 3). \]

Thus, the expression becomes

\[ \frac{8(m - 3)}{3 - m}. \]

Next, we notice that \(3 - m\) can be rewritten as \(-(m - 3)\). Therefore, we can rewrite the expression as:

\[ \frac{8(m - 3)}{-(m - 3)} = -8, \]

for \(m \neq 3\).

The excluded value occurs when the denominator is zero. Setting \(3 - m = 0\) gives us:

\[ m = 3. \]

Final Answer