ITOT 41 Autumn 2019 - THCS A - Additive practice Question 2

Two acute triangles $ABC,A_1B_1C_1$ satisfy $B_1,C_1\in BC$ and $A_1$ lies inside $ABC$. Their areas are $S,S_1$. Prove $\frac{S}{AB+AC}\gt \frac{S_1}{A_1B_1+A_1C_1}$.