Let F(x) = [(x² + 3x -4) / (x² - 4x + 3)]
Give a formula for the extended function that is continuous at x=1
Notice that
$\displaystyle \frac{x^2 + 3x -4}{x^2 - 4x + 3} = \frac{(x+4)(x-1)}{(x-3)(x-1)}$
so the terms $\displaystyle (x-1)$ will cancel provided that $\displaystyle x \ne 1$
So let us define the extended function $\displaystyle G(x)$ such that
$\displaystyle G(x) = \left\{\begin{array}{cc}\frac{x+4}{x-3},&\mbox{ if }
x \ne 1\\- \frac{5}{2}, & \mbox{ if } x=1.\end{array}\right.$