Решите уравнение: 1/(x-4)-1/(x+6)=5/28.

Ответ:

\[28 \cdot (x + 6) - 28 \cdot (x - 4) =\]

\[= 5 \cdot (x - 4)(x + 6)\]

\[28x + 168 - 28x + 112 =\]

\[= 5 \cdot \left( x^{2} + 2x - 24 \right)\]

\[280 = 5x^{2} + 10x - 120\]

\[5x^{2} + 10x - 120 - 280 = 0\]

\[5x² + 10x - 400 = 0\ \ \ |\ :5\]

\[x^{2} + 2x - 80 = 0\]

\[x_{1} + x_{2} = - 2;\ \ x_{1} \cdot x_{2} = - 80\]

\[x_{1} = 8,\ \ x_{2} = - 10\]

\[Ответ:\ x = 8;\ x = - 10.\]