1, a, đk x khác -1
\(P=\dfrac{x^2+x}{x^3+x^2+x+1}+\dfrac{1}{x^2+1}=\dfrac{x\left(x+1\right)}{x^2\left(x+1\right)+x+1}+\dfrac{1}{x^2+1}\)
\(=\dfrac{x\left(x+1\right)}{\left(x^2+1\right)\left(x+1\right)}+\dfrac{1}{x^2+1}=\dfrac{x}{x^2+1}+\dfrac{1}{x^2+1}=\dfrac{x+1}{x^2+1}\)
b, Với x = 1
\(P=\dfrac{1+1}{1^2+1}=\dfrac{2}{2}=1\)
2, đk x khác 0 ;-1
a, \(P=\dfrac{x^2}{x+1}+\dfrac{2\left(x-1\right)}{x}+\dfrac{x+2}{x^2+x}\)
\(=\dfrac{x^3+2\left(x^2-1\right)+x+2}{x\left(x+1\right)}=\dfrac{x^3+2x^2+x}{x\left(x+1\right)}=\dfrac{x^2+2x+1}{x+1}=x+1\)
b, Với x = 1
\(P=1+1=2\)