\(\frac{a-b}{\left(c-a\right)\left(c-b\right)}=\frac{\left(c-b\right)-\left(c-a\right)}{\left(c-a\right)\left(c-b\right)}=\frac{1}{c-a}-\frac{1}{c-b}=\frac{1}{c-a}+\frac{1}{b-c}\)
Tương tự:
\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}=\frac{1}{a-b}+\frac{1}{c-a};\frac{c-a}{\left(b-c\right)\left(a-b\right)}=\frac{1}{b-c}+\frac{1}{a-b}\)
Cộng lại có đpcm