Replace instances of f(x){\displaystyle f(x)\,} with the expression 1x{\displaystyle {\frac {1}{x}}} .
1x−1ax−a=(1x−1a)⋅1x−a{\displaystyle {\frac {{\frac {1}{x}}-{\frac {1}{a}}}{x-a}}=\left({\frac {1}{x}}-{\frac {1}{a}}\right)\cdot {\frac {1}{x-a}}}
=a−xxa(x−a)=(a−x)−xa(a−x)=−1ax{\displaystyle ={\frac {a-x}{xa(x-a)}}={\frac {(a-x)}{-xa(a-x)}}=-{\frac {1}{ax}}}
with the expression 
.
