Question

tìm x:

3x-7 chia hết cho x+2

Answer 1

\(\dfrac{3x-7}{x+2}=\dfrac{3x+6-13}{x+2}=\dfrac{3\left(x+2\right)}{x+2}-\dfrac{13}{x+2}\)

Nhẫn xét:

\(3\left(x+2\right)⋮\left(x+2\right)\\ \dfrac{3x-7}{x+2}⋮\left(x+2\right)\\ \Rightarrow13⋮\left(x+2\right)\\ hay.\left(x+2\right)\inƯ_{\left(13\right)}=\left\{-13;-1;1;13\right\}\\ \Rightarrow x\in\left\{-15;-3;-1;11\right\}\)

Answer 2

3x - 7 \(⋮\) x + 2
3.( x + 2) - 9 \(⋮\) x + 2 mà 3.(x + 2) \(⋮\) x + 2 => -9 \(⋮\) x + 2 
-> x + 2 \(\in\) Ư(-9) = { 1 ; -1 ; 3 ; -3 ; 9 ; -9 }
x + 2 = 1 
x       = 1 - 2
x       = -1 
x + 2 = -1 
x       = -1 - 2 
x       = -3 
x + 2 = ... rồi kết luận x \(\in\) { ..... }