ГДЗ по алгебре 8 класс Мерзляк Задание 100

\[\boxed{\text{100\ (100).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \frac{a + 7^{\backslash 3}}{12} + \frac{a - 4^{\backslash 4}}{9} =\]

\[= \frac{(a + 7) \cdot 3}{36} + \frac{(a - 4) \cdot 4}{36} =\]

\[= \frac{3a + 21 + 4a - 16}{36} =\]

\[= \frac{7a + 5}{36}\]

\[2)\ \frac{2b - 7c^{\backslash 5}}{6} - \frac{3b + 2c^{\backslash 2}}{15} =\]

\[= \frac{5(2b - 7c) - 2(3b + 2c)}{30} =\]

\[= \frac{10b - 35c - 6b - 4c}{30} =\]

\[= \frac{4b - 39c}{30}\]

\[3)\ \frac{3x - 2^{\backslash y}}{x} - \frac{3y - 1^{\backslash x}}{y} =\]

\[= \frac{y(3x - 2) - x(3y - 1)}{\text{xy}} =\]

\[= \frac{3xy - 2y - 3xy + x}{\text{xy}} =\]

\[= \frac{- 2y + x}{\text{xy}}\]

\[4)\ \frac{6p + 1^{\backslash 3}}{p} - \frac{2p + 8}{3p} =\]

\[= \frac{3(6p + 1) - 2p - 8}{3p} =\]

\[\text{=}\frac{18p + 3 - 2p - 8}{3p} = \frac{16p - 5}{3p}\]

\[5)\ \frac{5m - n}{14m} - \frac{m - 6n^{\backslash 2}}{7m} =\]

\[= \frac{5m - n - 2(m - 6n)}{14m} =\]

\[= \frac{5m - n - 2m + 12n}{14m} =\]

\[= \frac{3m + 11n}{14m}\]

\[6)\ \frac{x + 4^{\backslash y}}{11x} - \frac{y - 3^{\backslash x}}{11y} =\]

\[= \frac{y(x + 4) - x(y - 3)}{11xy} =\]

\[= \frac{xy + 4y - xy + 3x}{11xy} = \frac{3x + 4y}{11xy}\]

\[7)\ \frac{a + b^{\backslash c}}{\text{ab}} + \frac{a - c^{\backslash b}}{\text{ac}} =\]

\[= \frac{c(a + b) + b(a - c)}{\text{abc}} =\]

\[= \frac{ac + bc + ab - bc}{\text{abc}} =\]

\[= \frac{ac + ab}{\text{abc}} = \frac{a(c + b)}{\text{abc}} = \frac{c + b}{\text{bc}}\]

\[8)\ \frac{2}{p^{2}} + \frac{p - 1^{\backslash p}}{p} =\]

\[= \frac{2 + p(p - 1)}{p^{2}} = \frac{2 + p^{2} - p}{p^{2}}\]

\[9)\ \frac{k + 4^{\backslash k}}{k} - \frac{3k - 4}{k^{2}} =\]

\[= \frac{k(k + 4) - 3k + 4}{k^{2}} =\]

\[= \frac{k^{2} + 4k - 3k + 4}{k^{2}} =\]

\[= \frac{k^{2} + k + 4}{k^{2}}\]

\[10)\ \frac{x - y^{\backslash y}}{x^{3}} - \frac{y - {x^{2}}^{\backslash x}}{x^{2}y} =\]

\[= \frac{y(x - y) - x\left( y - x^{2} \right)}{x^{3}y} =\]

\[= \frac{xy - y^{2} - xy + x^{3}}{x^{3}y} = \frac{x^{3} - y^{2}}{x^{3}y}\]

\[11)\ \frac{2m - 3n^{\backslash n}}{m^{2}n} + \frac{7m - 2n^{\backslash m}}{mn^{2}} =\]

\[= \frac{n(2m - 3n) + m(7m - 2n)}{m^{2}n^{2}} =\]

\[= \frac{2mn - 3n^{2} + 7m^{2} - 2mn}{m^{2}n^{2}} =\]

\[= \frac{7m^{2} - 3n^{2}}{m^{2}n^{2}}\]

\[12)\ \frac{c + d^{\backslash c^{3}}}{cd^{4}} - \frac{c^{2} - 8d^{\backslash d}}{c^{3}d^{3}} =\]

\[= \frac{c^{2}(c + d) - d\left( c^{2} - 8d \right)}{c^{3}d^{4}} =\]

\[= \frac{c^{3} + c^{2}d - c^{2}d + 8d^{2}}{c^{3}d^{4}} =\]

\[= \frac{c^{3} + 8d^{2}}{c^{3}d^{4}}\]