Question

Rút gọn biểu thức:

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

Với a,b,c đôi 1 khác nhau

Answer 1

Quy đồng đi, ta sẽ được  \(A=0\)

Answer 2

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

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

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

\(A=\frac{0}{-\left(a-b\right)\left(a-c\right)\left(b-a\right)}\)

A = 0