I really don't understand this question.
If $\displaystyle f(x) = 1/x$, show that $\displaystyle f(a) - f(b) = f(ab/(b-a))$
Help would be greatly appreciated
Just transform the right hand side of this equation to the right hand side, by applying the definition of $\displaystyle f(x)$ and some quite routine algebraic transformations
$\displaystyle f(a)-f(b)=\frac{1}{a}-\frac{1}{b}=\ldots = \frac{1}{\frac{ab}{b-a}}=f\left(\frac{ab}{b-a}\right)$
and you are done.