Question

với 3 số a,b,c đôi một khác nhau , cmr : 

\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}\)+\(\frac{c-a}{\left(b-c\right)\left(b-a\right)}\)+\(\frac{a-b}{\left(c-a\right)\left(c-b\right)}\)= \(\frac{2}{a-b}\)+\(\frac{2}{b-c}\) + \(\frac{2}{c-a}\)

Answer 1

\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}=\frac{\left(a-c\right)-\left(a-b\right)}{\left(a-b\right)\left(a-c\right)}=\frac{1}{a-b}-\frac{1}{a-c}\)

\(\frac{c-a}{\left(b-c\right)\left(b-a\right)}=\frac{\left(b-a\right)-\left(b-c\right)}{\left(b-c\right)\left(b-a\right)}=\frac{1}{b-c}-\frac{1}{b-a}\)

\(\frac{a-b}{\left(c-a\right)\left(c-b\right)}=\frac{\left(c-b\right)-\left(c-a\right)}{\left(c-a\right)\left(c-b\right)}=\frac{1}{c-a}-\frac{1}{c-b}\)

Cộng theo vế ba đẳng trên được dpcm.

Answer 2

bn làm đúng rồi đó