\(A=\frac{2016a}{ab+2016a+2016}+\frac{b}{bc+b+2016}+\frac{c}{ac+c+1}\)

\(A=\frac{2016a}{ab+2016a+abc}+\frac{b}{bc+b+2016}+\frac{bc}{abc+bc+b}\)

\(A=\frac{2016a}{a\left(b+2016+bc\right)}+\frac{b}{bc+b+2016}+\frac{bc}{2016+bc+b}\)

\(A=\frac{2016}{b+2016+bc}+\frac{b}{bc+b+2016}+\frac{bc}{2016+bc+b}\)

\(A=\frac{2016+b+bc}{2016+b+bc}=1\)

Thay : 2016 = abc

ta có :

\(A=\frac{a^2bc}{ab+a^2bc+abc}+\frac{b}{bc+b+abc}+\frac{c}{ac+c+1}\)

\(A=\frac{a^2bc}{ab\left(1+ac+c\right)}+\frac{b}{b\left(c+1+ac\right)}+\frac{c}{ac+c+1}\)

\(A=\frac{ac}{ac+c+1}+\frac{1}{ac+c+1}+\frac{c}{ac+c+1}\)

\(A=\frac{ac+c+1}{ac+c+1}\)

\(A=1\)

vậy \(A=\frac{2016.a}{ab+2016.a+2016}+\frac{b}{bc+b+2016}+\frac{c}{ac+c+1}=1\)

Chúc bạn học tốt !

e ơi e nên tải tài liệu của võ quốc bá cẩn đi 

\(\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ca}{c+a}\)\(\Rightarrow\frac{a+b}{ab}=\frac{b+c}{bc}=\frac{c+a}{ac}\)\(\Rightarrow\frac{a}{ab}+\frac{b}{ab}=\frac{b}{bc}+\frac{c}{bc}=\frac{c}{ac}+\frac{a}{ac}\)

\(\Rightarrow\frac{1}{b}+\frac{1}{a}=\frac{1}{c}+\frac{1}{b}=\frac{1}{a}+\frac{1}{c}\)

Ta có:  +) \(\frac{1}{b}+\frac{1}{a}=\frac{1}{c}+\frac{1}{b}\)\(\Rightarrow\frac{1}{a}=\frac{1}{c}\)\(\Rightarrow a=c\)  (1)

+) \(\frac{1}{c}+\frac{1}{b}=\frac{1}{a}+\frac{1}{c}\)\(\Rightarrow\frac{1}{b}=\frac{1}{a}\)\(\Rightarrow b=a\)  (2)

Từ (1) và (2) => a = b = c

Lại có: \(P=\frac{\left(ab+bc+ac\right)^{1008}}{a^{2016}+b^{2016}+c^{2016}}=\frac{\left(a.a+a.a+a.a\right)^{1008}}{a^{2016}+a^{2016}+a^{2016}}=\frac{\left(a^2+a^2+a^2\right)^{1008}}{3.a^{2016}}\)

\(P=\frac{\left(3a^2\right)^{1008}}{3.a^{2016}}=\frac{3^{1008}.a^{2016}}{3.a^{2016}}=3^{1007}\)

\(ab+bc+ca=0\Rightarrow2ab+2bc+2ca=0\)

\(a+b+c=0\Rightarrow\left(a+b+c\right)^2=0\)

\(\Rightarrow a^2+b^2+c^2+2ab+2bc+2ca=0\)

Mà \(2ab+2bc+2ca=0\)

\(\Rightarrow a^2+b^2+c^2=0\)

Mà \(\hept{\begin{cases}a^2\ge0\\b^2\ge0\\c^2\ge0\end{cases}}\)

\(\Rightarrow a^2=b^2=c^2=0\)

\(\Rightarrow a=b=c=0\)

\(\Rightarrow P=1^{1945}+0^{1975}+\left(-1\right)^{2016}=2\)

Vậy ...

từ a+b+c = 0 => (a+b+c)²=0 => a²+b²+c²+2ab+2bc+2ac=0

từ ab+bc+ac = 0 => a²+b²+c² =0

=> a=b=c=0

=>P= 3

Tớ ko bt