Solve for: \lim_{x arrow 1} ((x^2-3x+2)/(x-1))

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Expression: $\lim_{x \rightarrow 1} \left(\frac{ {x}^{2}-3x+2 }{ x-1 }\right)$

Since evaluating limits of the numerator and denominator would result in an indeterminate form, use the L'Hopital's rule

$\lim_{x \rightarrow 1} \left(\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2}-3x+2 \right) }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( x-1 \right) }\right)$

Find the derivative

$\lim_{x \rightarrow 1} \left(\frac{ 2x-3 }{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( x-1 \right) }\right)$

Find the derivative

$\lim_{x \rightarrow 1} \left(\frac{ 2x-3 }{ 1 }\right)$

Any expression divided by $1$ remains the same

$\lim_{x \rightarrow 1} \left(2x-3\right)$

Evaluate the limit

$2 \times 1-3$

Simplify the expression

$-1$

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