Task B-1.6. Solve the equation

$$
\frac{x+3}{12(x+1)}:\left(\frac{2 x-3}{3 x-3}-\frac{3 x-1}{4 x+4}+\frac{x^{2}-7 x+14}{12 x^{2}-12}\right)=2015
$$
Solution. We solve the equation under the condition $x \neq 1$ and $x \neq -1$.

We reduce the expression in parentheses to the least common denominator and perform the indicated operations:

$$
\begin{aligned}
\frac{x+3}{12(x+1)}:\left(\frac{2 x-3}{3(x-1)}-\frac{3 x-1}{4(x+1)}+\frac{x^{2}-7 x+14}{12(x-1)(x+1)}\right) & =2015 \\
\frac{x+3}{12(x+1)}:\left(\frac{4(2 x-3)(x+1)-3(3 x-1)(x-1)+x^{2}-7 x+14}{12(x-1)(x+1)}\right) & =2015 \\
\frac{x+3}{12(x+1)}:\left(\frac{x-1}{12(x-1)(x+1)}\right) & =2015 \\
\frac{x+3}{12(x+1)}\left(\frac{12(x-1)(x+1)}{x-1}\right) & =2015 \\
x+3 & =2015 \\
x & =2012
\end{aligned}
$$