\(a.A=\left(\frac{x+2}{x^2-2x}+\frac{x-6}{x^2-4}-\frac{x-2}{x^2+2x}\right):\frac{2x-7}{x^2-4x+4}\\ \Leftrightarrow A=\left(\frac{x+2}{x\left(x-2\right)}+\frac{x-6}{\left(x+2\right)\left(x-2\right)}-\frac{x-2}{x\left(x+2\right)}\right):\frac{2x-7}{x^2-4x+4}\\ \Leftrightarrow A=\left(\frac{\left(x+2\right)\left(x+2\right)}{x\left(x+2\right)\left(x-2\right)}+\frac{x\left(x-6\right)}{x\left(x+2\right)\left(x-2\right)}-\frac{\left(x-2\right)\left(x-2\right)}{x\left(x+2\right)\left(x-2\right)}\right):\frac{2x-7}{x^2-4x+4}\\ \Leftrightarrow A=\left(\frac{\left(x+2\right)\left(x+2\right)+x\left(x-6\right)-\left(x-2\right)\left(x-2\right)}{x\left(x+2\right)\left(x-2\right)}\right):\frac{2x-7}{x^2-4x+4}\)
\(\Leftrightarrow A=\left(\frac{x^2+2x}{x\left(x+2\right)\left(x-2\right)}\right):\frac{2x-7}{x^2-4x+4}\\ \Leftrightarrow A=\frac{x\left(x+2\right)}{x\left(x+2\right)\left(x-2\right)}:\frac{2x-7}{x^2-4x+4}\\ \Leftrightarrow A=\frac{1}{x-2}:\frac{2x-7}{\left(x-2\right)^2}\\ \Leftrightarrow A=\frac{1}{x-2}.\frac{\left(x-2\right)^2}{2x-7}\\ \Leftrightarrow A=\frac{\left(x-2\right)^2}{\left(x-2\right)\left(2x-7\right)}\\ \Leftrightarrow A=\frac{x-2}{2x-7}\)
