KöMaL 2023 C1783

Let $a$, $b$, $c$ and $d$ be positive integers such that the open interval $\left(\frac{a}{b},\frac{c}{d}\right)$ includes $1$. Prove that $\frac{a}{b}<\frac{a+c+1}{b+d+1}<\frac{c}{d}.$