a) Muốn C \(\in\)Z thì x+12 \(⋮\)x+5
\(\Rightarrow\) x+5+7 \(⋮\)x+5
\(\Rightarrow\) 7 \(⋮\)x+5
\(\Rightarrow\) x+5 \(\in\){-7 ; -1 ; 1 ; 7}
TH1: x+5 = -7 \(\Rightarrow\) x= -12
TH2: x+5 = -1 \(\Rightarrow\) x= -6
TH3: x+5= 1 \(\Rightarrow\) x= -4
TH4: x+5= 7 \(\Rightarrow\)x= 2
Vậy x\(\in\){ -12 ; -6 ; -4 ; 2 } thì \(\frac{x+12}{x+5}\)có giá trị nguyên