Question

Evaluate:
`lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]`

Answer 1

`underset(xrarr1)"lim"[(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]`
`=underset(xrarr1)"lim"[(x-2)/(x(x-1))-(1)/(x(x^(2)-3x+2))]`
`=underset(Xrarr1)"lim"[(x-2)/(x(x-1))-(1)/(x(X-1)(x-2))]`
`=underset(xrarr1)"lim"[((x-2) ^(2)-1)/(x(x-1)(x-2))]`
`underset(xrarr1)"lim"((x-3)(x-1))/(x(x-1)(X-2))`
`=underset(xrarr1)"lim"(x-3)/(x(x-2))=(-2)/(1(-1))=2`.