Question

(\(\dfrac{1}{6}\)+\(\dfrac{1}{10}\)+\(\dfrac{1}{15}\)):(\(\dfrac{1}{6}\)+\(\dfrac{1}{10}\)-\(\dfrac{1}{15}\))/(\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{3}\)):(\(\dfrac{1}{4}\)-\(\dfrac{1}{6}\))

 

Answer 1

\(\dfrac{\left(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}\right):\left(\dfrac{1}{6}+\dfrac{1}{10}-\dfrac{1}{15}\right)}{\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{3}\right):\left(\dfrac{1}{4}-\dfrac{1}{6}\right)}\)

\(=\dfrac{\dfrac{5+3+2}{30}:\dfrac{5+3-2}{30}}{\left(\dfrac{3}{4}-\dfrac{2}{3}\right):\dfrac{1}{12}}\)

\(=\dfrac{\dfrac{10}{30}:\dfrac{6}{30}}{\dfrac{1}{12}:\dfrac{1}{12}}=\dfrac{10}{6}=\dfrac{5}{3}\)