\(\dfrac{x-7}{\left(x+2\right)\left(x-3\right)}>1\Leftrightarrow\dfrac{x-7-\left(x+2\right)\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}>0\)
\(\Leftrightarrow\dfrac{-\left(x-1\right)^2}{\left(x+2\right)\left(x-3\right)}>0\Rightarrow x\in\left(-2;3\right)\backslash\left\{1\right\}\)
\(\Rightarrow2c+a-3b=2.1+\left(-2\right)-3.3=-9\)
30
\(=sin\left(\dfrac{5\pi}{12}\right).sin\left(2x+\dfrac{\pi}{12}\right)-sin\dfrac{\pi}{12}.cos\left(2x+\dfrac{\pi}{12}\right)\)
\(=cos\left(\dfrac{\pi}{2}-\dfrac{5\pi}{12}\right)sin\left(2x+\dfrac{\pi}{12}\right)-sin\left(\dfrac{\pi}{12}\right)cos\left(2x+\dfrac{\pi}{12}\right)\)
\(=sin\left(2x+\dfrac{\pi}{12}\right)cos\left(\dfrac{\pi}{12}\right)-cos\left(2x+\dfrac{\pi}{12}\right)sin\left(\dfrac{\pi}{12}\right)\)
\(=sin\left(2x+\dfrac{\pi}{12}-\dfrac{\pi}{12}\right)=sin2x\)
\(\Rightarrow\left\{{}\begin{matrix}a=2\\b=0\end{matrix}\right.\) \(\Rightarrow b-2a=-4\)
