Try this
(%i15) assume_pos:true;
(%o15) true
(%i11) ratsimp((2*unit_step(x)-1)/x);
(%o11) 1/x
(%i12) assume_pos:false;
(%o12) false
(%i13) ratsimp((2*unit_step(x)-1)/x);
(%o13) (2*unit_step(x)-1)/x
In the first case the function simplifies to 1/x which is not correct. This function is always above the x axis for all
x. 1/x on the other hand is negative for x<0 and positive for x > 0 which is totally wrong. The answer in output %o13
is the only correct answer. This function does not simplify to 1/x.
Rich