\(P=\dfrac{2bc-2016}{3c-2bc+2016}-\dfrac{2b}{3-2b+ab}+\dfrac{4032-3ac}{3ac-4032+2016c}\)
\(=\dfrac{2bc-abc}{3c-2bc+abc}-\dfrac{2b}{3-2b+ab}+\dfrac{2abc-3ac}{3ac-2abc+a^2bc}\)
\(=\dfrac{2b-ab}{3-2b+ab}-\dfrac{2b}{3-2b+ab}+\dfrac{2b-3}{3-2b+ab}\)
\(=\dfrac{2b-ab-2b+2b-3}{3-2b+ab}\)
\(=\dfrac{-3+2b-ab}{3-2b+ab}=-1\).

Ta có:

\(+)\frac{2bc-2016}{3c-2bc+2016}=-1+\frac{3c}{3c-2bc+2016}\left(1\right)\)

\(+)\frac{-2b}{3-2b+ab}=\frac{-2bc}{3c-2bc+abc}=\frac{-2bc}{3c-2bc+2016}\left(2\right)\)

\(+)\frac{4032-3ac}{3ac-4032+2016a}=-1+\frac{2016a}{3ac-2abc+2016a}=-1+\frac{2016}{3c-2bc+2016}\left(3\right)\)

\(P=\left(1\right)+\left(2\right)+\left(3\right)=-1\)

Vậy .........

`(2bc-2016)/(3c-2bc+2016)`

`=(-(3c-2bc+2016)+3c)/(3c-2bc+2016)`

`=-1+(3c)/(3c-2bc+2016)`

`(2b)/(3-2b+ab)

`=(2bc)/(3c-2bc+abc)`

`=(2bc)/(3c-2bc+2016)`

`(4032-3ac)/(3ac-4032+2016a)`

`=(-(3ac-4032+2016a)+2016a)/(3ac-4032+2016a)`

`=-1+(2016a)/(3ac-2abc+2016a)`

`=-1+(2016)/(3c-2bc+2016)`

`=>M=-1+(3c)/(3c-2bc+2016)-(2bc)/(3c-2bc+2016)-1+(2016)/(3c-2bc+2016)

`=>M=-2+(3c-2bc+2016)/(3c-2bc+2016)`

`=>M=-2+1`

`=>M=-1`

`(2bc-2016)/(3c-2bc+2016)`

`=(-(3c-2bc+2016)+3c)/(3c-2bc+2016)`

`=-1+(3c)/(3c-2bc+2016)`

`(2b)/(3-2b+ab)`

`=(2bc)/(3c-2bc+abc)`

`=(2bc)/(3c-2bc+2016)`

`(4032-3ac)/(3ac-4032+2016a)`

`=(-(3ac-4032+2016a)+2016a)/(3ac-4032+2016a)`

`=-1+(2016a)/(3ac-2abc+2016a)`

`=-1+(2016)/(3c-2bc+2016)`

`=>M=-1+(3c)/(3c-2bc+2016)-(2bc)/(3c-2bc+2016)-1+(2016)/(3c-2bc+2016)`

`=>M=-2+(3c-2bc+2016)/(3c-2bc+2016)`

`=>M=-2+1`

`=>M=-1`

Nãy thiếu latex ạ sorry~~

Xúc xích bonitanwg 88%cặc

a. \(4ab.\frac{1}{3}ac-2aca-9a^2.\frac{1}{2}b+10a^2.\frac{1}{5}c+a^2b-a^2bc\)

\(=\left(4.\frac{1}{3}\right)\left(a.a\right).bc-2a^2c-\left(9.\frac{1}{2}\right)a^2b+\left(10.\frac{1}{5}\right)a^2c+a^2b-a^2bc\)

\(=\frac{4}{3}a^2bc-2a^2c-\frac{9}{2}a^2b+2a^2c+a^2b-a^2bc\)

\(=\left(\frac{4}{3}a^2bc-a^2bc\right)+\left(-2a^2c+2a^2c\right)+\left(-\frac{9}{2}a^2b+a^2b\right)\)

\(=\frac{1}{3}a^2bc+\left(-\frac{7}{2}a^2b\right)\)

b. \(2ab-2bc.c+ab+\frac{1}{2}c^2b-4cb^2+2bcb\)

\(=2ab-2bc^2+ab+\frac{1}{2}c^2b-4cb^2+2b^2c\)

\(=\left(2ab+ab\right)+\left(-2bc^2+\frac{1}{2}c^2b\right)+\left(-4cb^2+2b^2c\right)\)

\(=3ab+-\frac{3}{2}bc^2+-2b^2c\)

\(=b\left(3a-\frac{3}{2}c^2-2bc\right)\)

\(ab^3c^2-a^2b^2c^2+ab^2c^3-a^2bc^3\)

\(=abc^2\left(b^2-ab+abc-ac\right)\)

Dặt x=a, y=2b,z=3c

Khi đó

\(P=\frac{yz}{\sqrt{x+yz}}+\frac{xz}{\sqrt{y+xz}}+\frac{xy}{\sqrt{z+xy}}\)và x+y+z=1

Ta có \(\frac{yz}{\sqrt{x+yz}}=\frac{yz}{\sqrt{x\left(x+y+z\right)+yz}}=\frac{yz}{\sqrt{\left(x+y\right)\left(x+z\right)}}\le\frac{1}{2}yz\left(\frac{1}{x+y}+\frac{1}{x+z}\right)\)

=> \(P\le\frac{1}{2}\left(\frac{xz}{x+y}+\frac{yz}{x+y}\right)+\frac{1}{2}\left(\frac{xy}{y+z}+\frac{xz}{y+z}\right)+...=\frac{1}{2}\left(x+y+z\right)\)

                                                                                                                     \(=\frac{1}{2}\)

Vậy \(MaxP=\frac{1}{2}\)khi x=y=z=1/3 hay \(\hept{\begin{cases}a=\frac{1}{3}\\b=\frac{1}{6}\\c=\frac{1}{9}\end{cases}}\)