The curve in question is f(x) = e^x / x. To find the slope of the tangent line to this curve, we differentiate, using the quotient rule:
xe^x - e^x e^x(x-1)
f '(x) = ----------------- = --------------
x^2 x^2
at x=a=1, this slope is f '(1) = 0.
Find the value of the function at x = a =1: f(1) = e
Thus, the tangent line has slope 0 and passes thru (1,e). From this info we can readily surmise that the tangent line is horiz. and is given by y = e.
