Question

Tính hợp lí biết:

A = \(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\)

Answer 1

\(\dfrac{1}{A}=\dfrac{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}\)

\(=1-\dfrac{\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}=1-\dfrac{\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}{\dfrac{3.4+2.4-2.3}{2.3.4}}\)

\(=1-\dfrac{1}{3.4+2.4-2.3}=1-\dfrac{1}{14}=\dfrac{13}{14}\)

\(\Rightarrow A=\dfrac{14}{13}\)

Answer 2

ta có : 1/2+1/3-1/4 / 7/12-1/2.1/3.1/4= 7/12 / 13/24