(3x-1)+(7x-5)=1

Wie du siehst, kann man deine Gleichung auch auf unserem Rechner lösen.

Gruß radix !     ( und eine gute Nacht ! )

$${\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$$     = 1    

$${\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)\right)}}$$    = 1             2. Bruch mit 2 erweitert

3x-1 + 14x -10   = 1*2*(x+2)                          mit dem Nenner multipliziert

17x -11 = 2x + 4

15x = 15       =>      x = 1

Probe:     $${\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}} = {\mathtt{1}}$$

Gruß radix !       

vielen dank

Habe mich über dein DANKE gefreut und hoffe, dass du die einzelnen Schritte verstanden hast.

Gruß radix !