Bài 3:
\(VP=\dfrac{1}{a+1}+\dfrac{1}{a\left(a+1\right)}=\dfrac{a}{a\left(a+1\right)}+\dfrac{1}{a\left(a+1\right)}=\dfrac{a+1}{a\left(a+1\right)}=\dfrac{1}{a}=VT\)
Bài 4:
\(\dfrac{n+3}{n-2}=\dfrac{n-2+5}{n-2}=\dfrac{n-2}{n-2}+\dfrac{5}{n-2}=1+\dfrac{5}{n-1}\in Z\)
\(\Rightarrow5⋮n-2\)
\(\Rightarrow n-2\inƯ\left(5\right)=\left\{1;-1;5;-5\right\}\)
\(\Rightarrow n\in\left\{3;1;7;-3\right\}\)
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