A general idea is:
If x > 4, then
f(x) = (x+1+x-2)/(-(4-x)+2x) = (2x - 1)/(3x - 4)
If 2 < x <= 4, then
f(x) = (x+1+x-2)/(4-x+2x) = (2x - 1)/(x + 4)
If x < 2, then
f(x) = (x+1-(x-2))/(4-x+2x) = 3/(x + 4)
Now firstly, check for continuity at the breakpoints, i.e. 2,4...
Then secondly, justify why(or why not) the piecewise definitions are continuous.