a + b , \(N=\left(\frac{2}{x^2+x}+\frac{1}{x+1}\right):\frac{1}{x+1}\)ĐK : \(x\ne0;-1\)
\(=\left(\frac{2}{x\left(x+1\right)}+\frac{x}{x\left(x+1\right)}\right):\frac{1}{x+1}=\frac{x+2}{x\left(x+1\right)}.\frac{x+1}{1}=\frac{x+2}{x}\)
c, Ta có : \(\frac{x+2}{x}=1+\frac{2}{x}\)
Để N nguyên khi \(2⋮x\Rightarrow x\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
Vậy \(x=\pm1;\pm2\)thì N nguyên
d, ta có : \(N< 1\Rightarrow\frac{x+2}{x}< 1\Leftrightarrow\frac{x+2-x}{x}< 0\Rightarrow x< 0\)vì 2 > 0
bổ sung hộ mình
c, Kết hợp với đk vậy \(x=1;\pm2\)thì N nguyên
d, Kết hợp với đk vậy \(x< 0;x\ne-1\)
a) đk: \(\hept{\begin{cases}x\ne0\\x\ne-1\end{cases}}\)
b) \(N=\left(\frac{2}{x^2+x}+\frac{1}{x+1}\right)\div\frac{1}{x+1}\)
\(N=\frac{2+x}{x\left(x+1\right)}\cdot\left(x+1\right)=\frac{2+x}{x}\)
c) \(N=\frac{2+x}{x}=\frac{2}{x}+1\)
Để N nguyên \(x\inƯ\left(2\right)\Rightarrow x\in\left\{1;-2;2\right\}\)
d) \(N< 1\Leftrightarrow\frac{2}{x}+1< 1\Rightarrow\frac{2}{x}< 0\Rightarrow x< 0\)