Bruchgleichung: 1/6 - 2/3(1/(4x) - 1/(2x) - 1/4) = 1. Lösungsweg?

Question

Bruchgleichung lösen:

\( \frac{1}{6}-\frac{2}{3}\left(\frac{1}{4 x}-\frac{1}{2 x}-\frac{1}{4}\right)=1 \)

Lösungsweg?

Answer 1

 1/6 - 2/3(1/(4x) - 1/(2x) - 1/4) = 1  | + 2/3(1/(4x) - 1/(2x) - 1/4) - 1

 1/6 -1 = 2/3(1/(4x) - 1/(2x) - 1/4) 

-5/6 = 2/3(1/(4x) - 1/(2x) - 1/4)   | *6

-5 = 2*2 (1/(4x) - 1/(2x) - 1/4)       

-5 = 4 (1/(4x) - 1/(2x) - 1/4)  

-5 = 1/x - 2/x - 1       | + 1

-4 = -1/x         | *x

-4x = -1      |: (-4)

x = 1/4      

Kontrolle:

1/6 - 2/3(1/(4*(1/4)) - 1/(2*1/4)) - 1/4) = 1

1/6 - 2/3(1/1 - 1/(1/2) - 1/4) = 1

1/6 - 2/3(1 - 2 - 1/4) = 1

1/6 - 2/3(4/4 - 8/4 - 1/4) = 1

1/6 - 2/3*(-5/4) = 1

1/6 + 10/12 = 1

1/6 + 5/6 = 1 stimmt.