which expression is equivalent to the expression below?\n$\frac{m + 3}{m^{2}-16}div\frac{m^{2}-9}{m +…

which expression is equivalent to the expression below?\n$\frac{m + 3}{m^{2}-16}div\frac{m^{2}-9}{m + 4}$\n$\frac{1}{(m + 4)(m + 3)}$\n$\frac{1}{(m - 4)(m - 3)}$\n$\frac{m - 4}{m - 3}$\n$\frac{m + 3}{m + 4}$

which expression is equivalent to the expression below?\n$\frac{m + 3}{m^{2}-16}div\frac{m^{2}-9}{m + 4}$\n$\frac{1}{(m + 4)(m + 3)}$\n$\frac{1}{(m - 4)(m - 3)}$\n$\frac{m - 4}{m - 3}$\n$\frac{m + 3}{m + 4}$

Answer

Explanation:

Step1: Factor the expressions

We know that (m^{2}-16=(m + 4)(m - 4)) and (m^{2}-9=(m + 3)(m - 3)) according to the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)). The original complex - fraction (\frac{\frac{m + 3}{m^{2}-16}}{\frac{m^{2}-9}{m + 4}}) can be rewritten as (\frac{m + 3}{(m + 4)(m - 4)}\div\frac{(m + 3)(m - 3)}{m + 4}).

Step2: Change division to multiplication

Dividing by a fraction is equivalent to multiplying by its reciprocal. So (\frac{m + 3}{(m + 4)(m - 4)}\div\frac{(m + 3)(m - 3)}{m + 4}=\frac{m + 3}{(m + 4)(m - 4)}\times\frac{m + 4}{(m + 3)(m - 3)}).

Step3: Simplify the expression

Cancel out the common factors ((m + 3)) and ((m + 4)) in the numerator and denominator. We get (\frac{1}{(m - 4)(m - 3)}).

Answer:

(\frac{1}{(m - 4)(m - 3)})