Bài 1:
a) Ta có: \(\left(x+3\right)⋮\left(x-4\right)\)
\(\Rightarrow\left(x+3\right)-\left(x-4\right)⋮\left(x-4\right)\)
\(\Rightarrow\left(x+3-x+4\right)⋮\left(x-4\right)\)
\(\Rightarrow7⋮\left(x-4\right)\)
\(\Rightarrow\left(x-4\right)\inƯ\left(7\right)\)
\(\Rightarrow x-4\in\left\{-1;1;7;-7\right\}\)
\(\Rightarrow x\in\left\{3;5;11;-3\right\}\)
Vậy: \(x\in\left\{3;5;11;-3\right\}\)
b)
Ta có: x-5 là bội của 7-x
\(\Rightarrow\left(x-5\right)⋮\left(7-x\right)\)
\(\Rightarrow\left(x-5\right)+\left(7-x\right)⋮\left(7-x\right)\)
\(\Rightarrow\left(x-5+7-x\right)⋮\left(7-x\right)\)
\(\Rightarrow2⋮\left(7-x\right)\)
\(\Rightarrow\left(7-x\right)\inƯ\left(2\right)\)
\(\Rightarrow\left(7-x\right)\in\left\{-1;1;2;-2\right\}\)
\(\Rightarrow x\in\left\{8;6;5;9\right\}\)
Vậy: \(x\in\left\{8;6;5;9\right\}\)
