Sei x ∈ R ∖ Q {\displaystyle {}x\in \mathbb {R} \setminus \mathbb {Q} } und a , b , c , d ∈ Q {\displaystyle {}a,b,c,d\in \mathbb {Q} } . Zeige, dass aus a d − b c = 0 {\displaystyle {}ad-bc=0} entweder c x + d = 0 {\displaystyle {}cx+d=0} oder a x + b c x + d ∈ Q {\displaystyle {}{\frac {ax+b}{cx+d}}\in \mathbb {Q} } folgt.
