Question

X+3/2x-3 aparține lui Z.
Determinati x

Answer 1

$\dfrac{x+3}{2x-3} \rightarrow \dfrac{2\cdot (x+3)}{2x-3} = \dfrac{2x+6}{2x-3} = \dfrac{2x-3+9}{2x-3} = \\ \\ = \dfrac{2x-3}{2x-3}+\dfrac{9}{2x-3} = 1 +\dfrac{9}{2x-3} \\ \\ 2x-3 \in D_9 \Rightarrow 2x-3 \in \Big\{-9.-3.-1,1,3,9\Big\}\Big|+3 \Rightarrow \\ \\ \Rightarrow 2x \in \Big\{-6,0,2,4,6,12\Big\} \Big|:2 \Rightarrow \boxed{x \in \Big\{-3,0,1,2,3,6\Big\}}$