(i) \((\frac{-3}{7})\times (\frac{12}{13}+\frac{-5}{6})\)
= \(\frac{-3}{7}\times \frac{12}{13}+\frac{-3}{7}\times \frac{-5}{6}\)
= \(\frac{-36}{91}+\frac{15}{42}\)
= \(\frac{-36\times 6+15\times 13}{546}\)
= \(\frac{196-216}{546}\)
= \(\frac{-21}{546}\)
x x y + x x z = \(\frac{-1}{26}\)
\((\frac{-3}{7})\times (\frac{12\times 6-5\times 13}{78})\) = \(\frac{-3}{7}\times \frac{7}{78}\)
= \(\frac{-1}{26}\)
\((\frac{-3}{7})\times (\frac{12}{13}+\frac{-5}{6})\) = \((\frac{-3}{7}\times \frac{12}{13})\)+\((\frac{-3}{7}\times \frac{-5}{6})\)
(ii) \((\frac{-12}{5})\times (\frac{-15}{4}+\frac{8}{3})\)
= \(\frac{-12}{5}\times (\frac{-45+32}{12})\)
= \(\frac{13}{5}\)
x x y + x x z
\((\frac{-12}{5})\times (\frac{-15}{4})+(\frac{-12}{5})\times (\frac{8}{3})\)
\(\frac{45-32}{5}\) = \(\frac{13}{5}\)
(iii) \(\frac{-8}{3}\times (\frac{5}{6}+\frac{-13}{12})\) = \((\frac{-8}{3})\times (\frac{5}{6})+(\frac{-8}{3})\times (\frac{-13}{12})\)
\(\frac{-8}{3}\times (\frac{10-13}{12})\) = \(\frac{-40}{18}+\frac{104}{36}\)
\(\frac{24}{36}\) = \(\frac{-80+104}{36}\)
\(\frac{2}{
3}\) = \(\frac{2}{
3}\)
Therefore,
L.H.S = R.H.S
(iv) \(\frac{-3}{4}(\frac{-5}{2}+\frac{7}{6})\) = \((\frac{-3}{4})\times (\frac{-5}{2})+(\frac{-3}{4})\times (\frac{7}{6})\)
\(\frac{-3}{4}\times \frac{-5}{2}+\frac{-3}{4}\times \frac{7}{6}\) = \(\frac{-3}{4}(\frac{-5\times 6}{2\times 6}+\frac{7\times 6}{6\times 6})\)
\(\frac{15}{8}+\frac{-21}{24}\) = \(\frac{-3}{4}(\frac{7}{6}-\frac{5}{2})\)
\(\frac{45-21}{24}\) = \(\frac{-3}{4}(\frac{7}{6}-\frac{5\times 3}{2\times 3})\)
\(\frac{24}{24}\) = \(\frac{-3}{4}(\frac{7-15}{6})\)
\(\frac{24}{24}\) = \(\frac{24}{24}\)
1 = 1
Therefore,
L.H.S = R.H.S
