Algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.

 

Fill in the blanks to make a true equation:

\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} + \frac{E}{(x + 7)^2} + \frac{F}{(x + 7)^3}