\(f(x) = \left\{ \begin{array}{c l} \dfrac{-5x^{2}+4x+12}{-3x^{2}+x+10}, & \, x \neq 2 \\ C, & \, x = 2 \end{array} \right.\)
What value of C would make f(x) continuous at x = 2?
Factor the numerator as (5x + 6) ( - x + 2)
Factor the denominator as ( 3x + 5) ( -x + 2)
We are left with
(5x + 6) /( 3x + 5)
The value of C that makes this continuous at x = 2 is ( 5 (2) + 6) / (3(2) + 5) = 16 / 11
+73 
