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

b) \(\frac{x^2-xy}{5y^2-5xy}\)=\(\frac{x\left(x-y\right)}{-5y\left(x-y\right)}\)=\(\frac{-x}{5y}\)

c) \(\frac{3x^2-12x+12}{x^4-8x}\)=\(\frac{3\left(x^2-4x+4\right)}{x\left(x^3-2^3\right)}\)=\(\frac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+2x+4\right)}\)=\(\frac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)

Với đk trên ta có:

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

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

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

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

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

\(=\frac{x+y}{xy}\)

=\(\frac{30x^2y^3}{8x^2y^2}\)

Ta có :

\(\frac{6x^2y^2}{8xy^5}=\frac{3x}{4y^3}\)

\(\frac{x^2-xy}{5xy-5y^2}=\frac{x\left(x-y\right)}{5y\left(x-y\right)}=\frac{x}{5y}\)

Hok tốt !

\(\frac{6x^2y^2}{8xy^5}=\frac{6x^2y^2}{8xy^5}=\frac{6x}{8y^3}=\frac{3x}{4y^3}\)

\(\frac{x^2-xy}{5xy-5y^2}=\frac{x\left(x-y\right)}{5y\left(x-y\right)}=\frac{x}{5y}\)

A = x-y/x.(x+y) - 3x+y/x.(x-y) . (y-x)/x+y

   = x-y/x.(x+y) + 3x+y/x.(x+y)

   = x-y+3x+y/x.(x+y)

   = 4x/x.(x+y)

    = 4/x+y

Tk mk nha

\(A=\frac{x-y}{xy+y^2}-\frac{3x+y}{x^2-xy}.\frac{y-x}{x+y}\)

    \(=\frac{x-y}{y\left(x+y\right)}-\frac{3x+y}{x\left(x-y\right)}.\frac{-\left(x-y\right)}{x+y}\)

     \(=\frac{x-y}{y\left(x+y\right)}-\frac{-\left(3x+y\right).\left(x-y\right)}{x\left(x-y\right).\left(x-y\right)}\)

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

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

\(=\frac{x\left(x^2-2xy+y^2\right)+y\left(3x^2+4xy+y^2\right)}{xy\left(x^2-y^2\right)}\)

  \(=\frac{x^4-2x^2y+xy^2+3x^2y+4xy^2+y^3}{xy\left(x^2-y^2\right)}\)

\(=\frac{x^4+x^2y+5xy^2+y^3}{xy\left(x^2-y^2\right)}=\frac{x^2\left(x^2+y\right)+y^2\left(5x+y\right)}{xy\left(x^2-y^2\right)}\)

xin lỗi mình mới học lớp 7 thui ko giúp được gì cho bạn rồi 

Đk: x, y \(\ne\)0

Ta có: P = \(\frac{2}{x}-\left(\frac{x^2}{x^2+xy}+\frac{y^2-x^2}{xy}-\frac{y^2}{xy+y^2}\right)\cdot\frac{x+y}{x^2+xy+y^2}\)

P = \(\frac{2}{x}-\left(\frac{x^3+\left(y^2-x^2\right)\left(x+y\right)-y^3}{xy\left(x+y\right)}\right)\cdot\frac{x+y}{x^2+xy+y^2}\)

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

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

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

P = \(\frac{3x^2+xy+2y^2}{x\left(x^2+xy+y^2\right)}\)

b) Ta có: x² + y² + 10 = 2x - 6y

<=> x² - 2x + 1 + y² + 6y + 9 = 0

<=> (x - 1)² + (y + 3)² = 0

<=> \(\hept{\begin{cases}x-1=0\\y+3=0\end{cases}}\) <=> \(\hept{\begin{cases}x=1\\y=-3\end{cases}}\)

Do đó: P = \(\frac{3.1^2-3.1+2.\left(-3\right)^2}{1\left(1^2-3+\left(-3\right)^2\right)}=\frac{18}{7}\)

phải là x-y nha ko phải x^3 +.......-y^3

\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)

\(=\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)\left(x+y\right)^2}\)

\(=\frac{10y}{15\left(x+y\right)^2}\)

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

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

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

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

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

a)\(\frac{2xy}{3\left(x+y\right)^2}\)

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

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

câu a của công chúa xinh xắn còn thiếu nha

\(A=\left[\frac{x^2-y^2}{xy}-\frac{1}{xy}\left(\frac{x^2}{y}-\frac{y^2}{x}\right)\right]:\frac{x-y}{xy}\)

\(A=\left[\frac{x^2-y^2}{xy}-\left(\frac{x}{y^2}-\frac{y}{x^2}\right)\right].\frac{xy}{x-y}\) => \(A=\left(\frac{x^2-y^2}{xy}-\frac{x^3-y^3}{x^2y^2}\right).\frac{xy}{x-y}=\left(\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x^2y^2}\right).\frac{xy}{x-y}\)

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