Question

select the correct answer.

which expression is equivalent to the difference shown?

\\\frac{5}{m} - \frac{m - 8}{m^2 - 4m}\\

• \\(\frac{m - 3}{m^2 - 5m}\\)
• \\(\frac{4(m - 7)}{m(m - 4)}\\)
• \\(\frac{m + 13}{m^2 - 5m}\\)
• \\(\frac{4(m - 3)}{m(m - 4)}\\)

Explanation:

Find a common denominator

$$ \frac{5}{m} - \frac{m - 8}{m^2 - 4m} = \frac{5}{m} - \frac{m - 8}{m(m - 4)} $$

Combine the numerators over the common denominator

$$ \frac{5(m - 4) - (m - 8)}{m(m - 4)} = \frac{5m - 20 - m + 8}{m(m - 4)} $$

Simplify the numerator

$$ \frac{4m - 12}{m(m - 4)} = \frac{4(m - 3)}{m(m - 4)} $$

Answer:

• (A) \(\frac{m - 3}{m^2 - 5m}\)
• (B) \(\frac{4(m - 7)}{m(m - 4)}\)
• (C) \(\frac{m + 13}{m^2 - 5m}\)
• (D) \(\frac{4(m - 3)}{m(m - 4)}\) (Correct answer)