Draw the graph of `y=(1)/(x)+(1)/(x-2)`.

Explanation

We have `y=f(x)=(1)/(x)+(1)/(x-2)`
Clearly, vertical asymptotes are x = 0 , x = 2.
Also `f'(x)=-(1)/(x^(2))-(1)/((x-2)^(2)) lt 0`, so the function decreases.
For `x in(-oo,0)`
`underset(x rarr -oo)lim((1)/(x)+(1)/(x-2)=0` and `underset(xrarr0^(-))lim ((1)/(x)+(1)/(x-2))=-oo`
Thus, f(x) decreases from '0' to `'-oo'` in `(-oo,0)`
For `x in (2, oo)`
`unserset(x rarr 2^(+)) lim ((1)/(x)+(1)/(x-2))=oo` and `underset(xrarr oo)lim(1)/(x)+(1)/(x-2))=0`
Thus, f(x) decreases from `'oo'` to '0' in (`2,oo`).
Hence the graph of the function can be drawn as shown in the following figure.