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Дано
/ /297
| |—| |
| x / |
|———–|
|100000 |
|—— + 90|
0.001188 x / 120
——– – ————- – —–
x 250 x*500
10 + —
100
——————————–
1 1 1
——– + ———– + —
10 + x*0 100000 500
90 + ——
x
$$frac{- frac{297}{250 x left(90 + frac{100000}{x}right)} + frac{0.001188}{frac{x}{100} + 10} – 120 frac{1}{500 x}}{frac{1}{0 x + 10} + frac{1}{90 + frac{100000}{x}} + frac{1}{500}}$$
Подстановка условия
$$frac{- frac{297}{250 x left(90 + frac{100000}{x}right)} + frac{0.001188}{frac{x}{100} + 10} – 120 frac{1}{500 x}}{frac{1}{0 x + 10} + frac{1}{90 + frac{100000}{x}} + frac{1}{500}}$$
(0.001188/(10 + (-2)/100) – (297/(-2))/(100000/(-2) + 90)/250 – 120/(-2)*500)/(1/(10 + (-2)*0) + 1/(90 + 100000/(-2)) + 1/500)
$$frac{- frac{297}{250 (-2) left(90 + frac{100000}{(-2)}right)} + frac{0.001188}{frac{(-2)}{100} + 10} – 120 frac{1}{500 (-2)}}{frac{1}{0 (-2) + 10} + frac{1}{90 + frac{100000}{(-2)}} + frac{1}{500}}$$
(0.001188/(10 – 1/50) – (297/(-2))/(100000/(-2) + 90)/250 – 120/(-1000))/(1/(10 – 0) + 1/(90 + 100000/(-2)) + 1/500)
$$frac{- frac{-297}{frac{50000000}{-2} + 45000} + frac{0.001188}{- frac{1}{50} + 10} – – frac{3}{25}}{frac{1}{500} + frac{1}{frac{100000}{-2} + 90} + frac{1}{- 0 + 10}}$$
$$1.17775229583379$$
Степени
$$frac{1}{frac{51}{500} + frac{1}{90 + frac{100000}{x}}} left(frac{0.001188}{frac{x}{100} + 10} – frac{6}{25 x} – frac{297}{250 x left(90 + frac{100000}{x}right)}right)$$
Численный ответ
(0.001188/(10.0 + 0.01*x) – 0.24/x – 1.188/(x*(90.0 + 100000.0/x)))/(0.102 + 1/(90.0 + 100000.0/x))
Рациональный знаменатель
$$frac{- 1512000.0 x^{3} – 4363500000.0 x^{2} – 3000000000000 x}{25 x^{2} left(x + 1000right) left(50900 x + 51000000right)}$$
Объединение рациональных выражений
$$frac{x left(2376.0 x + 2673000.0right) – 600 left(x + 1000right) left(9 x + 10000right)}{5 x left(x + 1000right) left(509 x + 510000right)}$$
Общее упрощение
/ 2
-150000000000.0 + 218175000.0*x + 75600.0*x /
———————————————–
/ 2
x*63750000000.0 + 63625.0*x + 127375000.0*x/
$$- frac{75600.0 x^{2} + 218175000.0 x + 150000000000.0}{x left(63625.0 x^{2} + 127375000.0 x + 63750000000.0right)}$$
Собрать выражение
/ /297
| |—| |
| x / |
|———–|
|100000 |
|—— + 90|
0.001188 120 x /
——– – —– – ————-
x x*500 250
10 + —
100
——————————–
1 1 1
— + ——– + ———–
500 10 + x*0 100000
90 + ——
x
$$frac{- frac{297}{250 x left(90 + frac{100000}{x}right)} + frac{0.001188}{frac{x}{100} + 10} – 120 frac{1}{500 x}}{frac{1}{500} + frac{1}{0 x + 10} + frac{1}{90 + frac{100000}{x}}}$$
Общий знаменатель
/ 2
-1.0*54000000000.0 + 27216.0*x + 78543000.0*x/
————————————————
3 2
22905.0*x + 45855000.0*x + 22950000000.0*x
$$- frac{27216.0 x^{2} + 78543000.0 x + 54000000000.0}{22905.0 x^{3} + 45855000.0 x^{2} + 22950000000.0 x}$$
Комбинаторика
/ 2
-4.8*250000000.0 + 126.0*x + 363625.0*x/
——————————————
x*(1000 + x)*(510000 + 509*x)
$$- frac{604.8 x^{2} + 1745400.0 x + 1200000000.0}{x left(x + 1000right) left(509 x + 510000right)}$$
Раскрыть выражение
/ /297
| |—| |
| x / |
|———–|
|100000 |
|—— + 90|
6 0.001188 x /
– —- + ——– – ————-
25*x x 250
10 + —
100
———————————
1 1 1
——– + ———– + —
10 + x*0 100000 500
90 + ——
x
$$frac{- frac{297}{250 x left(90 + frac{100000}{x}right)} + frac{0.001188}{frac{x}{100} + 10} – frac{6}{25 x}}{frac{1}{0 x + 10} + frac{1}{90 + frac{100000}{x}} + frac{1}{500}}$$
