Question

cho phân số B=2m+3/m+1 với giá trị nào của m thì B nguyên

Answer 1

\(B=\dfrac{2\left(m+1\right)+1}{m+1}=2+\dfrac{1}{m+1}\)

Để B nguyên 

\(\Rightarrow\left(m+1\right)\inƯ\left(1\right)=\left\{\pm1\right\}\)

m+1     1         -1

m         0         -2

Answer 2

\(B=\dfrac{2m+3}{m+1}=\dfrac{2m+2+1}{m+1}=\dfrac{2\left(m+1\right)+1}{m+1}\)ư

\(B=\dfrac{2\left(m+1\right)}{m+1}+\dfrac{1}{m+1}=2+\dfrac{1}{m+1}\)

để \(B\in Z=>m+1\inƯ\left(1\right)=\left\{\pm1\right\}\)

\(\left\{{}\begin{matrix}m+1=1\\m+1=-1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=0\\m=-2\end{matrix}\right.\)

vậy \(m\in\left\{0;-2\right\}\left(thì\right)B\in Z\)

Answer 3