$\begin{array}{l}\dfrac{a}{b}=\dfrac{a-c}{c-b}\\↔a.(c-b)=b.(a-c)\\↔ac-ab=ab-bc\\↔ac+bc=2ab\\↔c.(a+b)=2ab\\↔a+b=\dfrac{2ab}{c}\\↔\dfrac{a+b}{2ab}=\dfrac{1}{c}\\↔\dfrac{1}{c}=\dfrac{1}{2}.(\dfrac{a}{ab}+\dfrac{b}{ab})\\↔\dfrac{1}{c}=\dfrac{1}{2}.(\dfrac{1}{a}+\dfrac{1}{b})(\text{luôn đúng với giả thiết})\\ hay \dfrac{a}{b}=\dfrac{a-c}{c-b}\\\underline{\text{CHÚC BẠN HỌC TỐT}}\\\end{array}$
