Question

Выполни действия

(m2−5m+2525m2−1⋅5m2+mm3+125−m+55m2−m):4m2+5m−25m+224−20m

Answer 1

$\dfrac{3}{4}.$

Объяснение:

$\bigg(\dfrac{m^2-5m+25}{25m^2-1} * \dfrac{5m^2+m}{m^3 + 125} - \dfrac{m+5}{5m^2-m}\bigg) : \dfrac{4}{m^2+5m} - \dfrac{25m+22}{4 -20m} = \dfrac{3}{4}. \\\\1)\ \dfrac{m^2-5m+25}{25m^2-1} * \dfrac{5m^2+m}{m^3 + 125} = \dfrac{m^2-5m+25}{(5m-1)(5m+1)} * \dfrac{m(5m+1)}{(m+5)(m^2-5m+25)} = \dfrac{1}{5m-1} * \dfrac{m}{m+5} = \dfrac{m}{(5m-1)(m+5)};\\\\\\2)\ \dfrac{m}{(5m-1)(m+5)} - \dfrac{m+5}{5m^2-m} = \dfrac{m^{/m}}{(5m-1)(m+5)} - \dfrac{m+5}{m(5m-1)} =\dfrac{m^2-(m+5)^2}{m(5m-1)(m+5)};\\\\\\$$3)\dfrac{m^2-(m+5)^2}{m(5m-1)(m+5)} : \dfrac{4}{m^2+ 5m} = \dfrac{m^2- m^2 -10m-25}{m(5m-1)(m+5)} * \dfrac{m(m+5)}{4} = \dfrac{-10m-25}{5m-1} * \dfrac{1}{4} = \dfrac{-10m-25}{4(5m-1)} = \dfrac{-10m-25}{20m-4}; \\\\\\4) \dfrac{-10m-25}{20m-4} - \dfrac{25m+22}{4-20m} = \dfrac{-10m-25}{20m-4} + \dfrac{25m+22}{20m-4} = \dfrac{-10m-25+25m+22}{20m-4} = \dfrac{15m-3}{20m-4} = \dfrac{3(5m-1)}{4(5m-1)} = \dfrac{3}{4}.$

Answer 2

ответ: $\dfrac{3}{4}$

Объяснение:

$\left(\dfrac{m^2-5m+25}{25m^2-1}\cdot \dfrac{5m^2+m}{m^3+125}-\dfrac{m+5}{5m^2-m}\right)\div \dfrac{4}{m^2+5m}-\dfrac{25m+22}{4-20m}=\\\\=\left(\dfrac{m^2-5m+25 }{(5m+1)(5m-1)}\cdot \dfrac{m(5m+1)}{(m+5)(m^{2}-5m+25 )}-\dfrac{m+5}{5m^{2} -m}\right) \cdot\dfrac{m^{2} +5m}{4}-\dfrac{25m+22}{4-20m}=\\\\=\left(\dfrac{m}{(5m-1)(m+5)}}-\dfrac{m+5}{m(5m-1)}\right) \cdot\dfrac{m(m+5)}{4}-\dfrac{25m+22}{4(1-5m)}=$$=\dfrac{m^{2}-(m+5)^{2} }{m(5m-1)(m+5)}} \: \cdot \: \dfrac{m(m+5)}{4}-\dfrac{25m+22}{4(1-5m)}=\dfrac{m^{2}-(m+5)^{2} }{4(5m-1)}}-\dfrac{25m+22}{4(1-5m)}=\\\\=\dfrac{-5(2m+5)}{4(5m-1)}}+\dfrac{25m+22}{4(5m-1)}=\dfrac{-10m-25+25m+22}{4(5m-1)} =\dfrac{15m-3}{4(5m-1)} =\\\\=\dfrac{3(5m-1)}{4(5m-1)} =\dfrac{3}{4}$