Task B-1.7. Solve the equation:

$$
\frac{2 x+1}{6 x^{2}-3 x}-\frac{2 x-1}{14 x^{2}+7 x}=\frac{8}{12 x^{2}-3}
$$
Solution. First, note that $x \neq 0, \pm \frac{1}{2}$.

(2 points)

$$
\begin{aligned}
& \frac{2 x+1}{3 x(2 x-1)}-\frac{2 x-1}{7 x(2 x+1)}=\frac{8}{3(2 x-1)(2 x+1)} / \cdot 21 x(2 x-1)(2 x+1) \\
& (2 x+1) \cdot 7 \cdot(2 x+1)-3(2 x-1)^{2}=8 \cdot 7 x \\
& 7\left(4 x^{2}+4 x+1\right)-3\left(4 x^{2}-4 x+1\right)-56 x=0 \\
& 28 x^{2}+28 x+7-12 x^{2}+12 x-3-56 x=0 \\
& 16 x^{2}-16 x+4=0 \\
& 4 x^{2}-4 x+1=0 \\
& (2 x-1)^{2}=0
\end{aligned}
$$

However, at the beginning, we noted that $x \neq \frac{1}{2}$, so the equation has no solution. (2 points)