How to evaluate the Limits by Factorization

In calculus, factorization is used for factoring the expressions in both numerator and denominator of the function. It helps us to find common factor in them and they both get cancelled mathematically. Later, the limit of the function can be evaluated easily by the direct substitution method. Here is the list of solved problems in which factorisation method is used to find the limits of the functions.

Evaluate $\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{x^2-3x+2}{x^2-5x+4}}$

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