Problem Solving (PS) | If f(w) = (1/w) + 1\(w+8) and the function f(w) equals 1/(w-1) then a

This math just looks time-consuming. It is not. Numbers are easy.*

\(f(w) =\frac{1}{w} + \frac{1}{w+8}\)

And\(f(w) = \frac{1}{w-1}\) . Set them equal.

\(\frac{1}{w-1} = \frac{1}{w} + \frac{1}{w+8}\)

\(\frac{1}{w-1} =
\frac{(w+8)+w}{w(w+8)}\)
\(\frac{1}{(w-1)} =
\frac{2w+8}{w^2+8w}\)
\((2w+8)(w-1) = w^2 + 8w\)
\(2w^2 - 2w + 8w - 8 = w^2 + 8w\)
\( w^2 - 2w - 8 =\)
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