Решите уравнение: 42/(x^2+5x)-3/(x^2-5x)=7/x.

Ответ:

\[\frac{42}{x^{2} + 5x} - \frac{3}{x^{2} - 5x} = \frac{7}{x}\text{\ \ \ \ \ }\]

\[42 \cdot (x - 5) - 3 \cdot (x + 5) =\]

\[= 7 \cdot (x - 5)(x + 5)\]

\[42x - 210 - 3x - 15 =\]

\[= 7 \cdot \left( x^{2} - 25 \right)\]

\[39x - 225 = 7x^{2} - 175\]

\[7x^{2} - 39x - 175 + 225 = 0\]

\[7x^{2} - 39x + 50 = 0\]

\[D = 1521 - 1400 = 121\]

\[x_{1} = \frac{39 + 11}{14} = \frac{50}{14} = \frac{25}{7} = 3\frac{4}{7};\ \ \ \]

\[x_{2} = \frac{39 - 11}{14} = \frac{28}{14} = 2.\]

\[Ответ:x = 3\frac{4}{7};\ \ x = 2.\]