Ответы
Ответ дал:
0
Раскладываем каждый знаменатель на множители
х³+5х²-25х-125=х²(х+5)-25(х+5)=(х+5)(х²-25)=(х+5)(х-5)(х+5)
25-10х+х²=(5-х)²=(х-5)²
х²+10х+25=(х+5)²
Общий знаменатель:
(х+5)(х-5)(х+5)(х-5)
Умножаем первую дробь на (х-5), вторую дробь на (х+5)², третью дробь на (х-5)²
![\frac{10}{(x+5)(x-5)(x+5)} - \frac{1}{(x-5) ^{2} }+ \frac{1}{(x+5) ^{2} }= \\ \\ =\frac{10(x-5)}{(x+5)(x-5)(x+5)(x-5)} - \frac{(x+5) ^{2} }{(x-5) ^{2}(x+5) ^{2} }+ \frac{(x-5)^{2} }{(x+5) ^{2}(x-5) ^{2} }= \frac{10}{(x+5)(x-5)(x+5)} - \frac{1}{(x-5) ^{2} }+ \frac{1}{(x+5) ^{2} }= \\ \\ =\frac{10(x-5)}{(x+5)(x-5)(x+5)(x-5)} - \frac{(x+5) ^{2} }{(x-5) ^{2}(x+5) ^{2} }+ \frac{(x-5)^{2} }{(x+5) ^{2}(x-5) ^{2} }=](https://tex.z-dn.net/?f=+%5Cfrac%7B10%7D%7B%28x%2B5%29%28x-5%29%28x%2B5%29%7D+-+%5Cfrac%7B1%7D%7B%28x-5%29+%5E%7B2%7D+%7D%2B+%5Cfrac%7B1%7D%7B%28x%2B5%29+%5E%7B2%7D+%7D%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B10%28x-5%29%7D%7B%28x%2B5%29%28x-5%29%28x%2B5%29%28x-5%29%7D+-+%5Cfrac%7B%28x%2B5%29+%5E%7B2%7D+%7D%7B%28x-5%29+%5E%7B2%7D%28x%2B5%29+%5E%7B2%7D++%7D%2B+%5Cfrac%7B%28x-5%29%5E%7B2%7D+%7D%7B%28x%2B5%29+%5E%7B2%7D%28x-5%29+%5E%7B2%7D++%7D%3D+++)
![=\frac{10(x-5)-(x+5) ^{2}+(x-5)^{2} }{(x+5) ^{2}(x-5) ^{2} }= \\ \\ =\frac{10x-50-x ^{2}-10x-25+x^{2}-10x+25 }{(x+5) ^{2}(x-5) ^{2} }= \frac{-10x-50 }{(x+5) ^{2}(x-5) ^{2} }= \\ \\ = \frac{-10(x+5) }{(x+5) ^{2}(x-5) ^{2} }=- \frac{10}{(x+5)(x-5) ^{2} } =\frac{10(x-5)-(x+5) ^{2}+(x-5)^{2} }{(x+5) ^{2}(x-5) ^{2} }= \\ \\ =\frac{10x-50-x ^{2}-10x-25+x^{2}-10x+25 }{(x+5) ^{2}(x-5) ^{2} }= \frac{-10x-50 }{(x+5) ^{2}(x-5) ^{2} }= \\ \\ = \frac{-10(x+5) }{(x+5) ^{2}(x-5) ^{2} }=- \frac{10}{(x+5)(x-5) ^{2} }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%28x-5%29-%28x%2B5%29+%5E%7B2%7D%2B%28x-5%29%5E%7B2%7D+%7D%7B%28x%2B5%29+%5E%7B2%7D%28x-5%29+%5E%7B2%7D++%7D%3D+++%5C%5C++%5C%5C+%3D%5Cfrac%7B10x-50-x+%5E%7B2%7D-10x-25%2Bx%5E%7B2%7D-10x%2B25+%7D%7B%28x%2B5%29+%5E%7B2%7D%28x-5%29+%5E%7B2%7D++%7D%3D++%5Cfrac%7B-10x-50+%7D%7B%28x%2B5%29+%5E%7B2%7D%28x-5%29+%5E%7B2%7D++%7D%3D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B-10%28x%2B5%29+%7D%7B%28x%2B5%29+%5E%7B2%7D%28x-5%29+%5E%7B2%7D++%7D%3D-+%5Cfrac%7B10%7D%7B%28x%2B5%29%28x-5%29+%5E%7B2%7D+%7D+)
х³+5х²-25х-125=х²(х+5)-25(х+5)=(х+5)(х²-25)=(х+5)(х-5)(х+5)
25-10х+х²=(5-х)²=(х-5)²
х²+10х+25=(х+5)²
Общий знаменатель:
(х+5)(х-5)(х+5)(х-5)
Умножаем первую дробь на (х-5), вторую дробь на (х+5)², третью дробь на (х-5)²
Вас заинтересует
1 год назад
1 год назад
1 год назад
6 лет назад