Evaluate the following limit: _ x 4 x^2-7x+12 x^2 -3x-4 - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}^2-7\text{x}+12}{{\text{x}^2}-3\text{x}-4}$

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Answer

$\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}^2-7\text{x}+12}{{\text{x}^2}-3\text{x}-4}$ $=\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}^2-3\text{x}-4\text{x}+12}{\text{x}^2+\text{x}-4\text{x}-4}$ $=\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}(\text{x}-3)-4(\text{x}-3)}{\text{x}(\text{x}+1)-1(\text{x}+1)}$ $=\lim\limits_{\text{x}\rightarrow4}\frac{(\text{x}-3)(\text{x}-4)}{(\text{x}-4)(\text{x}+1)}$ $=\lim\limits_{\text{x}\rightarrow4}\frac{\text{x}-3}{\text{x}+1}$ $=\frac{4-3}{4+1}$ $=\frac15$

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