The domain of the function f(x)

$f(x)=\frac{x^{2}+1}{x^{2}-3 x+2}$

f(x) is defined if x2 − 3x + 2 ≠ 0

i.e  f(x) is not defined 

for  x2 − 3x + 2 = 0

i.e x2 − 2x − x + 2 = 0

(x2 − 2x) −1 (x − 2) = 0

 x (x − 2) −1 (x − 2) = 0

i.e (x − 1) (x − 2) = 0

i.e x = 1 or x = 2

i.e for x = 1 or x = 2,  f (x) is not defined 

∴ Domain of f(x) = R ~ {1,2}