Question

what is (x + 7) to the -2 power divided by (x to the 2nd power - 49) to the -1 power

Answer 1

It's easier to answer if you write it algebraically. Note that

x^2-49 = (x+7)(x-7)
Note also that dividing by
(x^2-49)^-1 is the same as multiplying by (x^2 -49) or(x+7)(x-7)

Therefore

1/(x+7)^2 * (x+7)(x-7) = (x-7)/(x+7)