Given that \( a=6, b=-4 \) and \( c=2 \), evaluate: \( \frac{a+2 b}{c}+\frac{b}{a-c} \)

To evaluate the expression \( \frac{a+2b}{c} + \frac{b}{a-c} \) given \( a=6, b=-4, c=2 \), we can substitute the values of \( a, b, \) and \( c \) into the expression. First, calculate \( a + 2b \): \[ a + 2b = 6 + 2(-4) = 6 - 8 = -2 \] Next, we can calculate \( a - c \): \[ a - c = 6 - 2 = 4 \] Now we substitute these results into the expression: \[ \frac{a + 2b}{c} = \frac{-2}{2} = -1 \] \[ \frac{b}{a - c} = \frac{-4}{4} = -1 \] Finally, combine these results: \[ -1 + (-1) = -2 \] Therefore, the final evaluation of the expression is: \[ \boxed{-2} \]