Question

cho A= [ ( 1 /x^2+x ) - ( 2-x / x+1 ) ] . ( 3x /1-2x+x^2 )

a,Rút gọn

b,Tìm x thuộc z để A thuộc z

c,Tìm x để A<0

Answer 1

https://i.imgur.com/nGzcVuS.jpg

Answer 2

ĐK: \(x\ne0;\pm1\)

\(A=\left(\dfrac{1}{x\left(x+1\right)}-\dfrac{2-x}{x+1}\right).\dfrac{3x}{1-2x+x^2}\)

\(A=\left(\dfrac{1-x\left(2-x\right)}{x\left(x+1\right)}\right).\dfrac{3x}{1-2x+x^2}=\dfrac{\left(1-2x+x^2\right)}{x\left(x+1\right)}\dfrac{3x}{1-2x+x^2}=\dfrac{3}{x+1}\)

b/ Để \(A\in Z\Rightarrow3⋮\left(x+1\right)\Rightarrow x+1=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(x+1=-3\Rightarrow x=-4\)

\(x+1=-1\Rightarrow x=-2\)

\(x+1=1\Rightarrow x=0\left(l\right)\)

\(x+1=3\Rightarrow x=2\)

c/ \(A< 0\Leftrightarrow\dfrac{3}{x+1}< 0\Leftrightarrow x+1< 0\Rightarrow x< -1\)