\(x=\dfrac{3}{4}+\dfrac{1}{2}-\dfrac{2}{3}=\dfrac{9+6-8}{12}=\dfrac{7}{12}\)
\(A=\dfrac{3.4.5...101}{2.3.4...100}=\dfrac{101}{2}\)
\(x-\dfrac{1}{2}+\dfrac{2}{3}=\dfrac{3}{4}\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{2}{3}\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{12}\\ \Rightarrow x=\dfrac{1}{12}+\dfrac{1}{2}\\ \Rightarrow x=\dfrac{7}{12}\)
\(A=\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{4}\right)\times...\times\left(1+\dfrac{1}{100}\right)\\ \Rightarrow A=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\text{}\text{}\text{}...\times\dfrac{101}{100}\\ \Rightarrow A=\dfrac{101}{2}\)
