Đáp án:
`1/{(a+b)(b+c)(a+c)}`
Giải thích các bước giải:
`{a^2(b-c)+b^2(c-a)+c^2(a-b)}/{a^4(b^2-c^2)+b^4(c^2-a^2)+c^4(a^2-b^2)}`
`={a^2b-a^2c+b^2c-ab^2+c^2(a-b)}/{a^4b^2-a^4c^2+b^4c^2-a^2b^4+c^4(a^2-b^2)}`
`={a^2b-ab^2-(a^2c-b^2c)+c^2(a-b)}/{(a^4b^2-a^2b^4)-(a^4c^2-b^4c^2)+c^4(a^2-b^2)}`
`={ab(a-b)-c(a^2-b^2)+c^2(a-b)}/{a^2b^2(a^2-b^2)-c^2(a^4-b^4)+c^4(a^2-b^2)}`
`={ab(a-b)-c(a+b)(a-b)+c^2(a-b)}/{a^2b^2(a^2-b^2)-c^2(a^2+b^2)(a^2-b^2)+c^4(a^2-b^2)`
`={(a-b)(ab-ac-bc+c^2)}/{(a^2-b^2)(a^2b^2-a^2c^2-b^2c^2+c^4)}`
`={(a-b)[a(b-c)-c(b-c)]}/{(a^2-b^2)[a^2(b^2-c^2)-c^2(b^2-c^2)]}`
`={(a-b)(b-c)(a-c)}/{(a^2-b^2)(b^2-c^2)(a^2-c^2)}`
`={(a-b)(b-c)(c-a)}/{(a+b)(a-b)(b+c)(b-c)(a+c)(a-c)}`
`=1/{(a+b)(b+c)(a+c)}`
