To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.
To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.
Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.
... y = 1 + 1/((x -1)(x -4))
If you like, this can be "simplified" to ...
... y = (x² -5x +5)/(x² -5x +4)
In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).
18/5 is basically 3 3/5 as a mixed number. When you convert a fraction to a decimal, you always want the denominator to either 10, 100, or 1000 so that the number is accurate. And so you multiply the denominator by what ever number will get 10, 100 or 1000, in which in this case is 10 when you multiply by 2. Multiply the numerator(3) by 2 so that it will be the same value. You should now have 3 6/10. After that, since 6/10 is basically 60/100, take out the 100 and move the decimal unit 2 units to the left of 60. And since you still have the whole number three, your final answer will be 3.6.