`a)` \(\left(\dfrac{4}{15}+\dfrac{3}{5}\right):\dfrac{5}{6}+\left(\dfrac{11}{15}-\dfrac{8}{5}\right):\dfrac{5}{6}\)
\(=\left(\dfrac{4}{15}+\dfrac{9}{15}\right)\cdot\dfrac{6}{5}+\left(\dfrac{11}{15}-\dfrac{24}{15}\right)\cdot\dfrac{6}{5}\)
\(=\dfrac{13}{15}\cdot\dfrac{6}{5}-\dfrac{13}{15}\cdot\dfrac{6}{5}\)
\(=\dfrac{6}{5}\cdot\left(\dfrac{13}{15}-\dfrac{13}{15}\right)=0\)
`b)` \(\left(\dfrac{7}{15}-\dfrac{7}{5}+\dfrac{8}{15}+\dfrac{2}{5}\right)\cdot\dfrac{2021}{2022}\)
\(=\left(\dfrac{7}{15}-\dfrac{21}{15}+\dfrac{8}{15}+\dfrac{6}{15}\right)\cdot\dfrac{2021}{2022}\)
`=0*2021/2022=0`
`c)` \(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right)\cdot\left(\dfrac{4}{5}-\dfrac{3}{4}\right)^2\)
\(=\left(\dfrac{12}{12}+\dfrac{8}{12}-\dfrac{3}{12}\right)\cdot\left(\dfrac{16}{20}-\dfrac{15}{20}\right)^2\)
\(=\dfrac{17}{12}\cdot\dfrac{1}{400}\)
`=17/4800`
(4/15 + 3/5 ) : 5/6 +(11/15 -8/5 ) : 5/6
=4/15 + 3/5 : 5/6 + 11/15 -8/5 : 5/6
=5/6.(4/15 +3/5 +11/15 -8/5)
= 5/6.((4/15 +11/15)+ (3/5 -8/5))
=5/6.((1 +(- 1 ))
= 5/6 .0
=0
