đã tắt máy chưa để cho mình giải nha

Giúp mik nha mọi người :)

Chưa tắt máy, ai giúp mik giải với!!!

\(B=\frac{x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)}{x^2y-x^2z+y^2z-y^3}\)

\(=\frac{x^2y-x^2z+zy^2-xy^2+z^2x-z^2y}{x^2\left(y-z\right)-y^2\left(y-z\right)}\)

\(=\frac{\left(x^2y-z^2y\right)-\left(xy^2-zy^2\right)-\left(x^2z-z^2x\right)}{\left(x^2-y^2\right)\left(y-z\right)}\)

\(=\frac{\left[y\left(x+z\right)-y^2-xz\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)

\(=\frac{\left(xy+zy-y^2-xz\right)\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)

\(=\frac{\left[\left(xy-y^2\right)-\left(xz-zy\right)\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)

\(=\frac{\left[y\left(x-y\right)-z\left(x-y\right)\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)

\(=\frac{\left(y-z\right)\left(x-y\right)\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)

\(=\frac{x-z}{x+y}\)

\(A=\frac{\left(x^2-y\right)\left(y+1\right)+x^2y^2-1}{\left(x^2+y\right)\left(y+1\right)+x^2y^2+1}\)

\(=\frac{x^2y-y^2+x^2-y+x^2y^2-1}{x^2y+y^2+x^2+y+x^2y^2+1}\)

\(=\frac{\left(x^2y+x^2\right)+\left(x^2y^2-y^2\right)-\left(y+1\right)}{\left(x^2y+x^2\right)+\left(x^2y^2+y^2\right)+\left(y+1\right)}\)

\(=\frac{x^2\left(y+1\right)+y^2\left(x^2-1\right)-\left(y+1\right)}{x^2\left(y+1\right)+y^2\left(x^2+1\right)+\left(y+1\right)}\)

\(=\frac{\left(x^2-1\right)\left(y+1\right)+y^2\left(x^2-1\right)}{\left(x^2+1\right)\left(y+1\right)+y^2\left(x^2+1\right)}\)

\(=\frac{\left(x^2-1\right)\left(y^2+y+1\right)}{\left(x^2+1\right)\left(y^2+y+1\right)}\)

\(=\frac{x^2-1}{x^2+1}\)

=3x-3y+y-2x+z-x-2y+z

=(3x-2x-x)-(3y-y+2y)+(z+z)

=0-4y+2z

=2z-4y

giải hết ra lun và đáp số bằng mấy

rút gọn =2*z-4*y

phân tích nhân tử=2*(z-2*y)

\(\frac{xy+2x+1}{xy+x+y+1}+\frac{yz+2y+1}{yz+y+z+1}+\frac{zx+2z+1}{zx+z+x+1}\)

Ta có: \(\frac{xy+2x+1}{xy+x+y+1}=\frac{\left(xy+x\right)+\left(x+1\right)}{\left(xy+x\right)+\left(y+1\right)}=\frac{x\left(y+1\right)+\left(x+1\right)}{\left(y+1\right)\left(x+1\right)}=\frac{x}{x+1}+\frac{1}{y+1}\)

Tương tự ta có:

\(\frac{yz+2y+1}{yz+y+z+1}=\frac{y}{y+1}+\frac{1}{z+1}\)

\(\frac{zx+2z+1}{zx+z+x+1}=\frac{z}{z+1}+\frac{1}{x+1}\)

Từ đây ta có biểu thức ban đầu sẽ bằng

\(\frac{x}{x+1}+\frac{1}{y+1}+\frac{y}{y+1}+\frac{1}{z+1}+\frac{z}{z+1}+\frac{1}{x+1}\)

\(\left(\frac{x}{x+1}+\frac{1}{x+1}\right)+\left(\frac{y}{y+1}+\frac{1}{y+1}\right)+\left(\frac{z}{z+1}+\frac{1}{z+1}\right)=1+1+1=3\)

CHÚ Ý: ab+a+b+1=a(b+1)+(b+1)=(a+1)(b+1)

Xét: \(\frac{xy+2x+1}{xy+x+y+1}=\frac{x\left(y+1\right)+x+1}{\left(x+1\right)\left(y+1\right)}=\frac{x}{x+1}+\frac{1}{y+1}\)

Tương tự với 2 biểu thức còn lại ta được:

A=\(\frac{x}{x+1}+\frac{1}{y+1}+\frac{y}{y+1}+\frac{1}{z+1}+\frac{z}{z+1}+\frac{1}{x+1}\)

=\(\frac{x+1}{x+1}+\frac{y+1}{y+1}+\frac{z+1}{z+1}=1+1+1=3\)

Cặp đôi hoàn hảo luôn song hành

 (x - y + z)^2 + (z - y)^2 + (x - y + z)(2y -2z)

\(<=>(x-y+z)^2+2(x-y+z)(y-z)+(z-y)^2\)

\(<=> (x-y+z+z-y)^2<=> ( x-2y-2z)^2\)

\(\left(x+y+z\right)^2+\left(z-y\right)^2+\left(x-y+z\right)\left(2y-2z\right)\)

\(=\left(x+y+z+y-z\right)^2\)

\(=\left(x+2y\right)^2\)

\(\frac{2x+2y-z}{z}=\frac{2x-y+2z}{y}=\frac{-x+2y+2z}{x} \)

=>\(\frac{2x+2y-z}{z}+3=\frac{2x-y+2z}{y}+3=\frac{-x+2y+2z}{x}+3\)

=>\(\frac{2x+2y+2z}{z}=\frac{2x+2y+2z}{y}=\frac{2x+2y+2z}{x}\)

=>\(\frac{x+y+z}{z}=\frac{x+y+z}{y}=\frac{x+y+z}{x}\)

=>\(\orbr{\begin{cases}x+y+z=0\\x=y=z\end{cases}}\)

Với \(x+y+z=0\Rightarrow\hept{\begin{cases}x+y=-z\\y+z=-x\\x+z=-y\end{cases}}\)

\(\Rightarrow M=\frac{\left(x+y\right)\left(y+z\right)\left(x+z\right)}{8xyz}=\frac{-xyz}{8xyz}=-\frac{1}{8}\)

Với \(x=y=z\)\(\Rightarrow M=\frac{\left(x+y\right)\left(y+z\right)\left(x+z\right)}{8xyz}=\frac{2x.2y.2z}{8xyz}=\frac{8xyz}{8xyz}=1\)

Trả lời:

g) G = ( 3x + 5 ).( 2x - 1 ) + ( 4x - 1 ).( 3x + 2 ) 

= 6x² - 3x + 10x - 5 + 12x² + 8x - 3x - 2 

= 18x² + 12x - 7

Ta có: | x | = 2 => x = 2 hoặc x = - 2

Thay x = 2 vào G, ta có:

G = 18.2² + 12.2. - 7 = 89

Thay x = - 2 vào G, ta có:

G = 18.(- 2 )² + 12.( - 2 ) - 7 = 41

h) H = ( 2x + y ).( 2z + y ) + ( x - y ).( y - z ) 

= 4xz + 2xy + 2yz + y² + xy - xz - y² + yz

= 3xz + 3xy + 3yz 

Ta có: z = | 1 | = 1

Thay x = 1; y = 1; z = 1 vào H, ta có:

H = 3.1.1 + 3.1.1 + 3.1.1 = 9