\(\dfrac{7}{18}\).(\(\dfrac{-12}{23}\)-\(\dfrac{4}{15}\))+\(\dfrac{7}{18}\).(\(\dfrac{8}{30}\)+\(\dfrac{35}{23}\))
= \(\dfrac{7}{18}\).[\(\dfrac{-12}{23}\)-\(\dfrac{4}{15}\)+\(\dfrac{8}{30}\)+\(\dfrac{35}{23}\)]
= \(\dfrac{7}{18}\).[(\(\dfrac{-12}{23}\)+\(\dfrac{35}{23}\))-(\(\dfrac{4}{15}\)+\(\dfrac{4}{15}\))]
= \(\dfrac{7}{18}\).[1-\(\dfrac{8}{15}\)] = \(\dfrac{7}{18}\).\(\dfrac{7}{15}\) = \(\dfrac{49}{270}\)\(\dfrac{7}{18}.\left(\dfrac{-12}{23}-\dfrac{4}{15}\right)+\dfrac{7}{18}.\left(\dfrac{8}{30}+\dfrac{35}{23}\right)\)
\(=\dfrac{7}{18}.\left(\dfrac{-12}{23}-\dfrac{4}{15}+\dfrac{8}{30}+\dfrac{35}{23}\right)\)
\(=\dfrac{7}{18}.\left[\left(\dfrac{-12}{23}+\dfrac{35}{23}\right)+\left(\dfrac{-4}{15}+\dfrac{8}{30}\right)\right]\)
\(=\dfrac{7}{18}.\left[1+0\right]\)
\(=\dfrac{7}{18}.1\)
\(=\dfrac{7}{18}\)