Question

find the coordinates of the point where the graph of the following function intersects the x axis y=x^2-5x+6/x-2

Answer 1

$\stackrel{\textit{x-intercept occurs when y = 0}}{\stackrel{y}{0}=\cfrac{x^2-5x+6}{x-2}}\implies 0=x^2-5x+6\implies 0=(x-3)(x-2) \\\\\\ x= \begin{cases} 3\\ 2 \end{cases}\qquad \qquad \stackrel{coordinates}{(3~~,~~0)\qquad (2~~,~~0)}$