\(=\dfrac{x^2+2x-x-2}{x^2-3x-2x-6}\cdot\dfrac{x^2+4x-3x-12}{x^2+4x-x-4}\cdot\dfrac{y^2-5y+3y-15}{y^2-5y+2y-10}\cdot\dfrac{\left(y-2\right)\left(y+2\right)}{y^2+3y-2y-6}\)
\(=\dfrac{x\left(x+2\right)-\left(x+2\right)}{x\left(x-3\right)-2\left(x-3\right)}\cdot\dfrac{x\left(x+4\right)-3\left(x+4\right)}{x\left(x+4\right)-\left(x+4\right)}\cdot\dfrac{y\left(y-5\right)+3\left(y-5\right)}{y\left(y-5\right)+2\left(y-5\right)}\cdot\dfrac{\left(y-2\right)\left(y+2\right)}{y\left(y+3\right)-2\left(y+3\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)}{\left(x-3\right)\left(x-2\right)}\cdot\dfrac{\left(x+4\right)\left(x-3\right)}{\left(x+4\right)\left(x-1\right)}\cdot\dfrac{\left(y-5\right)\left(y+3\right)}{\left(y-5\right)\left(y+2\right)}\cdot\dfrac{\left(y-2\right)\left(y+2\right)}{\left(y+3\right)\left(y-2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+4\right)\left(x-3\right)\left(y-5\right)\left(y+3\right)\left(y-2\right)\left(y+2\right)}{\left(x-3\right)\left(x-2\right)\left(x+4\right)\left(x-1\right)\left(y-5\right)\left(y+2\right)\left(y+3\right)\left(y-2\right)}\)
\(=\dfrac{\left(x+2\right)}{\left(x-2\right)}\)
