Surely it is simpler to jus note that if x= 1, the denominator is 0 so the fraction is not defined.

. It does NOT contradict the statement you give because the statement includes the condition "c> 0". Here c is -1 and is not greater than 0.is this contradictory to what we are all taught that 'in the case of f(x+c) and c>0 then the graph will be of f(x) translated c units to the NEGATIVE direction of the x-axis'. ?????

would this be due to the negative nature of x in f(x)?