Question

. Determinati numerele intregi x pentru care fractia 6 supra 2x-1 este nr.intreg.

Answer 1

6/2x-1⇒2x-1∈{-6,-3,-2,-1,0,1,2,3,6}
2x-1=-6⇒2x=-5⇒x=$\frac{-5}{2}$ ∉Z
2x-1=-3⇒2x=-2⇒x=-1∈Z
2x-1=-2⇒2x=-1⇒x=$\frac{-1}{2}$ ∉Z
2x-1=-1⇒2x=0⇒x=0∈Z
2x-1=0⇒2x=1⇒x=$\frac{1}{2}$ ∉Z
2x-1=1⇒2x=2⇒x=1∈Z
2x-1=2⇒2x=3⇒x=$\frac{3}{2}$
2x-1=3⇒2x=4⇒x=2∈Z
2x-1=6⇒2x=7⇒x=$\frac{7}{2}$
x∈{-1;0;1;2}