Question

$\underset{x\to 5}{\lim }\frac{x^2-9x+20}{x^2-6x+5}$

Answer 1

$$\begin{gathered} \underset{x\to 5}{\lim }\left[\frac{x^2-9x+20}{x^2-6x+5}\right] \\ \mathrm{It}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{0}{0}. \\ \underset{x\to 5}{\lim }\left[\frac{x^2-4x-5x+20}{x^2-x-5x+5}\right] \\ =\underset{x\to 5}{\lim }\left[\frac{x\left(x-4\right)-5\left(x-4\right)}{x\left(x-1\right)-5\left(x-1\right)}\right] \\ =\underset{x\to 5}{\lim }\left[\frac{\left(x-5\right)\left(x-4\right)}{\left(x-1\right)\left(x-5\right)}\right] \\ =\frac{5-4}{5-1} \\ =\frac{1}{4} \end{gathered}$$