Question
Evaluate the limits using limit properties. If a limit does not exist, state why.$$\lim _{x \rightarrow 1} \frac{x^{2}-4 x+3}{x^{2}-2 x+1}$$
Step 1
The numerator $x^{2}-4x+3$ can be factored as $(x-3)(x-1)$ and the denominator $x^{2}-2x+1$ can be factored as $(x-1)(x-1)$ or $(x-1)^2$. So, the expression becomes: $$\lim _{x \rightarrow 1} \frac{(x-3)(x-1)}{(x-1)^2}$$ Show more…
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