Let $a_1, a_2, b_2, b_3, c_1, c_2$ be positive numbers such that $a_1b_1-c^2_1 > 0$ and $a_2b_2-c^2_2> 0$. Prove that $$\frac{8}{(a_1 + a_2)(b_1 + b_2)- (c_1 + c_2)^2 } \le \frac{1}{a_1b_1-c^2_1}+\frac{1}{a_2b_2-c^2_2}$$