Characteristic polynomial of an inverse matrix

Let $A$ be a $2 \times 2$ real matrix, such that trace of $A$ is 5 and determinant of $A$ is 6. If the characteristic polynomial of $(A + I_2)^{-1}$ is $x^2 - bx + c$, where $I_2$ is the $2 \times 2$ identity matrix, then $\frac{b}{c}$ equals ________ (in integer).