Question

\(D=\dfrac{-\dfrac{2}{3}+\dfrac{3}{4}-2}{\dfrac{2}{3}-\dfrac{3}{4}-2}\times\dfrac{\dfrac{-2}{3}-\dfrac{3}{4}-2}{\dfrac{2}{3}+\dfrac{3}{4}+2}\)

Answer 1

\(D=\dfrac{-\dfrac{2}{3}+\dfrac{3}{4}-2}{\dfrac{2}{3}-\dfrac{3}{4}-2}\times\dfrac{-\dfrac{2}{3}-\dfrac{3}{4}-2}{\dfrac{2}{3}+\dfrac{3}{4}+2}\\ =\dfrac{-\left(\dfrac{2}{3}-\dfrac{3}{4}+2\right)}{\dfrac{2}{3}-\dfrac{3}{4}-2}\times\dfrac{-\left(\dfrac{2}{3}+\dfrac{3}{4}+2\right)}{\dfrac{2}{3}+\dfrac{3}{4}+2}\\ =\dfrac{-\left(\dfrac{8}{12}-\dfrac{9}{12}+\dfrac{24}{12}\right)}{\dfrac{8}{12}-\dfrac{9}{12}-\dfrac{24}{12}}\times\left(-1\right)\\ =\dfrac{8-9+24}{12}:\dfrac{8-9-24}{12}\\ =\dfrac{8-9+24}{8-9-24}\\ =-\dfrac{23}{25}\)