Sure, let's solve the given proportion step-by-step to derive the correct equation.
Given:
[tex]\[
\frac{32}{x-8} = \frac{24}{x-10}
\][/tex]
To remove the denominators, we can cross-multiply:
[tex]\[
32 \cdot (x - 10) = 24 \cdot (x - 8)
\][/tex]
Now, let's expand both sides of the equation:
[tex]\[
32(x - 10) = 24(x - 8)
\][/tex]
Expanding both sides gives:
[tex]\[
32x - 320 = 24x - 192
\][/tex]
So, the equation derived after removing the denominators and simplifying is:
[tex]\[
32x - 320 = 24x - 192
\][/tex]
Therefore, the correct answer is:
[tex]\[
32x - 320 = 24x - 192
\][/tex]
