a: \(-2y^2-5y+2xy+5x\)
=-y(2y+5)+x(2y+5)
=(2y+5)(-y+x)
\(y^3+x-y-xy^2\)
\(=y\left(y^2-1\right)-x\left(y^2-1\right)\)
\(=\left(y^2-1\right)\left(y-x\right)\)
\(\frac{-2y^2-5y+2xy+5x}{y^3+x-y-xy^2}\)
\(=\frac{\left(2y+5\right)\left(-y+x\right)}{\left(y^2-1\right)\left(y-x\right)}=\frac{\left(-2y-5\right)\left(y-x\right)}{\left(y^2-1\right)\left(y-x\right)}=\frac{-2y-5}{y^2-1}\)
b: \(x^2y^2+1+\left(x^2-y\right)\left(1-y\right)\)
\(=x^2y^2+1+x^2-x^2y-y+y^2\)
\(=x^2\left(y^2+1\right)+\left(y^2+1\right)-y\left(x^2+1\right)\)
\(=\left(y^2+1\right)\left(x^2+1\right)-y\left(x^2+1\right)=\left(x^2+1\right)\left(y^2-y+1\right)\)
\(x^2y^2+1+\left(x^2+y\right)\left(1+y\right)\)
\(=x^2y^2+1+x^2+x^2y+y+y^2\)
\(=x^2\left(y^2+1\right)+\left(y^2+1\right)+y\cdot\left(x^2+1\right)=\left(x^2+1\right)\left(y^2+1\right)+y\left(x^2+1\right)\)
\(=\left(x^2+1\right)\left(y^2+y+1\right)\)
Ta có: \(\frac{x^2y^2+1+\left(x^2-y\right)\left(1-y\right)}{x^2y^2+1+\left(x^2+y\right)\left(1+y\right)}\)
\(=\frac{\left(x^2+1\right)\left(y^2-y+1\right)}{\left(x^2+1\right)\left(y^2+y+1\right)}=\frac{y^2-y+1}{y^2+y+1}\)
