Question

2x+5chia het cho x+1

 

Answer 1

Ta có:

\(\frac{2x+5}{x+1}=\frac{x+x+5}{x+1}=\frac{x+1+4+x}{x+1}=1+\frac{4+x}{1+x}=1+\frac{1+3+x}{x+1}=2+\frac{3}{x+1}\)

\(\Rightarrow\left(2x+5\right)⋮\left(x+1\right)\Leftrightarrow\left(x+1\right)\inƯ_{\left(3\right)}\)

Mà Ư(3) = { -3, -1, 1, 3}

Nếu x + 1 = -3 => x = -3 -  1 = -4

x + 1 = -1 => x = -1 -  1 = -2

x + 1 = 1 => x = 1 -  1 = 0

x + 1 = 3 => x = 3 - 1 = 2

Vậy x \(\in\){ -4, -2, 0, 2}