Question

select the correct answer.

what is the simplest form of \\(\frac{4m - 17}{m^2 - 16} + \frac{3m - 11}{m^2 - 16}\\) assuming no denominator equals zero?

\\(\circ\\) \\(\frac{7}{m + 4}\\)

\\(\circ\\) \\(\frac{7m}{m + 4}\\)

\\(\circ\\) \\(\frac{7}{m - 4}\\)

\\(\circ\\) \\(\frac{7m - 6}{m^2 - 16}\\)

Explanation:

Combine the numerators over the common denominator

$$ \frac{4m - 17}{m^2 - 16} + \frac{3m - 11}{m^2 - 16} = \frac{(4m - 17) + (3m - 11)}{m^2 - 16} = \frac{7m - 28}{m^2 - 16} $$

Factor the numerator and the denominator

$$ \frac{7(m - 4)}{(m - 4)(m + 4)} $$

Simplify the rational expression

$$ \frac{7}{m + 4} \quad (m eq 4) $$

Answer:

• (A) \(\frac{7}{m+4}\) (Correct answer)
• (B) \(\frac{7m}{m+4}\)
• (C) \(\frac{7}{m-4}\)
• (D) \(\frac{7m-6}{m^2-16}\)