Выбрав удобный способ, вычислите значение выражения:решите объяснением.[latex] \frac{4}{ 5* 6} + \frac{4}{6 * 7} + \frac{4}{7 * 8} + \frac{4}{8 * 9} [/latex]

[latex] \frac{4}{5*6} + \frac{4}{6*7}+ \frac{4}{7*8}+ \frac{4}{8*9}= \frac{16}{45} \\ \\ 1) \frac{4}{5*6} + \frac{4}{6*7}= \frac{4*7}{5*6*7} + \frac{4*5}{5*6*7}= \frac{28+20}{5*6*7} = \frac{48}{5*6*7} = \frac{6*8}{5*6*7} = \frac{8}{5*7} \\ \\ 2)\frac{4*9}{7*8*9}+ \frac{4*7}{7*8*9}= \frac{36+28}{7*8*9} = \frac{64}{7*8*9} = \frac{8*8}{7*8*9} = \frac{8}{7*9} \\ \\ 3) \frac{8*9}{5*7*9} + \frac{8*5}{5*7*9} = \frac{72+40}{5*7*9} = \frac{112}{5*7*9} = \frac{7*16}{5*7*9} = \frac{16}{5*9 } = \frac{16}{45} [/latex]