2.)Berechne und vereinfache:
a.) \[\left(-\frac{1} {7} +\frac{1}{5}\right):\frac{204}{125}\] b.) \[\left(\frac{1} {4} -\frac{1}{3}\right)\cdot\left(-\frac{12} {7} -\frac{12}{5}\right)\] c.) \[-\frac{133} {131} +\frac{133}{129}\]
ohne GTR.
Lösungen:

2a.) \[\begin {matrix} \left(-\frac{1} {7} +\frac{1}{5}\right):\frac{204}{125} & = & \left(-\frac{5} {35} +\frac{7}{35}\right):\frac{204}{125} \\ & = & \frac{2} {35} \cdot \frac{125}{204} \\ & = & \frac{1} {7} \cdot \frac{25}{102} \\ & = & \frac{25} {714} \end {matrix} \]

2b.) \[\begin {matrix} \left(\frac{1} {4} -\frac{1}{3}\right)\cdot\left(-\frac{12} {7} -\frac{12}{5}\right) & = & \left(\frac{3} {12} -\frac{4}{12}\right)\cdot\left(-\frac{60} {35} -\frac{84}{35}\right) \\ & = & \frac{-1} {12} \cdot \frac{-144}{35} \\ & = & \frac{1} {1} \cdot \frac{12}{35} \\ & = & \frac{12} {35} \end {matrix} \]

2c.)
NR: 129 ⋅ 131 = 16899
       
     129
   387
  129
    1   
  16899
Alternative: \(131 \cdot 129 = (130 +1)(130-1)=130^2-1^2=16900-1=16899\)

Also: \[\begin {matrix} -\frac{133} {131} +\frac{133}{129} & = & \frac{-129 \cdot 133} {129 \cdot 131} +\frac{131 \cdot 133}{131 \cdot 129} \\ & = & \frac{-129 \cdot 133 + 131 \cdot 133}{16899} \\ & = & \frac{(-129+131) \cdot 133} {16899} \\ & = & \frac{(2) \cdot 133} {16899} = \frac{266} {16899} \end {matrix} \]