Let's solve [tex]$\frac{8 m^2 - 56 m}{m - 7}$[/tex] step-by-step to simplify this expression.
1. Factor the numerator:
The given numerator is [tex]\(8 m^2 - 56 m\)[/tex]. Notice that we can factor an [tex]\(8m\)[/tex] out of this expression:
[tex]\[
8 m^2 - 56 m = 8m(m - 7)
\][/tex]
2. Rewrite the expression with the factored numerator:
Substitute the factored form of the numerator back into the original fraction:
[tex]\[
\frac{8 m^2 - 56 m}{m - 7} = \frac{8m(m - 7)}{m - 7}
\][/tex]
3. Simplify the fraction:
Since [tex]\(m \neq 7\)[/tex], we can cancel out [tex]\((m - 7)\)[/tex] from the numerator and the denominator:
[tex]\[
\frac{8m(m - 7)}{m - 7} = 8m
\][/tex]
Thus, the simplified form of the given expression is [tex]\(8m\)[/tex].
Given the answer choices:
A) [tex]\(\frac{2 m-1}{4 m}\)[/tex]
B) [tex]\(\frac{3 m-10}{7}\)[/tex]
C) [tex]\(\frac{10}{5 m-6}\)[/tex]
D) [tex]\(8 m\)[/tex]
The correct choice is:
D) [tex]\(8m\)[/tex].
