Question

Determinati valorile intregi ale lui x pentru care avem: 10/x apartine Z
-5/ x-7 apartine Z
19/ 3x-2 apartine Z
2x+5/ x-2 apartine Z

Answer 1

a)$- \frac{5}{x-7} \in Z=\ \textgreater \ x-7|5=\ \textgreater \ x-7\in \{-5,-1,1,5\}|+7 \\ x\in \{2,6,8,12\}$
b)$\frac{19}{3x-2} \in Z =\ \textgreater \ 3x-2|19 \\ 3x-2\in \{-19,-1,1,19\}=\ \textgreater \ 3x\in\{-17,1,3,21\} \\ x\in\{1,7\}$
c) $\frac{2x+5}{x-2} \in Z =\ \textgreater \ \\ x-2|2x+5 \\ x-2|x-2|\cdot 2 \\ x-2|2x+5 \\ x-2|2x-4 \\ x-2|2x+5-2x+4 \\ x-2|9 \\ x-2\in\{-9,-1,1,9\} \\ x\in\{-7,1,3,11\}$