a^2=bc
=>a*a=b/c
=>a/b=c/a=k
=>a=bk; c=ak
\(\dfrac{2022a+2021b}{2023a-2024b}=\dfrac{2022\cdot bk+2021b}{2023\cdot bk-2024b}=\dfrac{2022k+2021}{2023k-2024}\)
\(\dfrac{2022c+2021a}{2023c-2024a}=\dfrac{2022ak+2021a}{2023ak-2024a}=\dfrac{2022k+2021}{2023k-2024}\)
=>\(\dfrac{2022a+2021b}{2023a-2024b}=\dfrac{2022c+2021a}{2023c-2024a}\)