a: ĐKXĐ: x<>-1; y<>1; x<>-y
\(P=\dfrac{-x^2}{\left(x+y\right)\left(y-1\right)}-\dfrac{y^2}{\left(x+y\right)\left(x+1\right)}+\dfrac{x^2y^2}{\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{-x^3-x^2-y^3+y^2+x^2y^2\left(x+y\right)}{\left(x+y\right)\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{-x^3-x^2-y^3+y^2+x^3y^2+x^2y^3}{\left(x+y\right)\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{-\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\left(x-y\right)+x^2y^2\left(x+y\right)}{\left(x+y\right)\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{-x^2+xy-y^2-x+y+x^2y^2}{\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{-x^2\left(1-y^2\right)-y\left(y-1\right)+x\left(y-1\right)}{\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{x^2\left(y-1\right)\left(y+1\right)+\left(y-1\right)\left(-y+x\right)}{\left(x+1\right)\left(y-1\right)}\)
\(=\dfrac{x^2\left(y+1\right)+\left(x-y\right)}{x+1}\)
c: Để P=2 thì x^2y+x^2+x-y=2x+2
=>x^2y+x^2+x-y-2x-2=0
=>x^2y+x^2-x-y-2=0
=>x=-1 và y=-1(loại)
