Question

Rút gọn phân thức sau: \(\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)

Answer 1

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

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

\(=\dfrac{\left(a-b\right)\left(ab-ca-cb+c^2\right)}{\left(a-b\right)\left(b-c\right)\left(b+c\right)}\)

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