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