Ответы
Ответ:
To solve the equation \( \frac{6x - 9}{1 - 3x} + \frac{6x + 1}{3x + 1} = \frac{2}{9x^2 - 1} \), let's first find a common denominator and combine the fractions:
The common denominator is \( (1 - 3x)(3x + 1)(9x^2 - 1) \).
\[ (6x - 9)(3x + 1) + (6x + 1)(1 - 3x) = 2 \]
Now, expand and simplify:
\[ (18x^2 - 24x - 9) + (6x - 18x - 6x^2 - 1) = 2 \]
Combine like terms:
\[ -7x^2 - 36x - 10 = 2 \]
Move all terms to one side of the equation:
\[ -7x^2 - 36x - 12 = 0 \]
Now, we can use the quadratic formula to find the solutions:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For \(-7x^2 - 36x - 12\), where \(a = -7\), \(b = -36\), and \(c = -12\). Calculate the discriminant \(b^2 - 4ac\) and proceed accordingly.
Note: The solutions might involve complex numbers since the discriminant could be negative.