\(=-2\left(-\dfrac{2}{1\cdot2}+\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{8\cdot9}\right)\\ =-2\left(-\dfrac{2}{2}+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ =-2\left(-1+1-\dfrac{1}{9}\right)=-2\left(-\dfrac{1}{9}\right)=\dfrac{2}{9}\)