if you meant (x+2)/(x-1) [add the bracket when using wolframalpha] , then it has
a vert. aymt. at x=1 cos x-1 can't be 0, consider limits-from 1+ve side (like 1.01+2/1.01-1) , it's +ve infinity , consider the other side of 1 (like 0.99+2/0.99-1), it's -ve infinity
a hor. asyt. at...