Question

Thực hiện phép tính:   1/ (a - b).(b - c) - 1/(a - c)(b - c) - 1/ (a - b)(a - c)

Answer 1

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

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

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

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

Answer 2

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

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

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

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

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

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

=0