1: |x-3|=4
=>x-3=4 hoặc x-3=-4
=>x=7 hoặc x=-1
Khi x=7 thì \(A=\dfrac{7+2}{7}=\dfrac{9}{7}\)
Khi x=-1 thì \(A=\dfrac{-1+2}{-1}=-1\)
2: \(B=\dfrac{x-1}{x}+\dfrac{2x+1}{x\left(x+1\right)}\)
\(=\dfrac{x^2-1+2x+1}{x\left(x+1\right)}=\dfrac{x\left(x+2\right)}{x\left(x+1\right)}=\dfrac{x+2}{x+1}\)
3.
\(P=\dfrac{A}{B}=\dfrac{x+2}{x}:\dfrac{x+2}{x+1}=\dfrac{\left(x+2\right)\left(x+1\right)}{x\left(x+2\right)}=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}\)
Để P nguyên thì \(\dfrac{1}{x}\in Z\)
\(\Rightarrow x\in U\left(1\right)=\left\{\pm1\right\}\)
\(\Rightarrow x=1;-1\)
