3x-5 là bội của x+4=>3x-5\(⋮\)x+4=>\(\frac{3x-5}{x+4}\)=\(\frac{3x-5+12-12}{x+4}=3+\frac{-17}{x+4}\)=>\(x+4\inƯ\left(-17\right)=\left(\pm1;\pm17\right)\)
Ta có Bảng
x+4 | 1 | -1 | 17 | -17 |
x | -3 | -4 | 13 | -20 |
\(3x-5\in B(x+4)\)
\(\Rightarrow(3x-5)⋮(x+4)\)\(\Rightarrow(3x+3\times4-12-5)⋮(x+4)\)
\(\Rightarrow[3\times(x+4)-17]⋮(x+4)\)mà \([3\times(x+4)]⋮(x+4)\)
\(\Rightarrow17⋮(x+4)\)\(\Rightarrow x+4\in\text{Ư}(17)\)
\(\Rightarrow x+4\in-1;1;-17;17\)
\(\Rightarrow x\in-5;-3;-21;13\)