Дано
$$frac{left(frac{1}{1500} + frac{10}{x}right) left(5 + frac{1000000}{x}right)}{frac{x}{100} + left(5 + frac{1000000}{x}right) left(frac{x}{1000} + 15right) + 200 + frac{10000000}{x}}$$
Подстановка условия
$$frac{left(frac{1}{1500} + frac{10}{x}right) left(5 + frac{1000000}{x}right)}{frac{x}{100} + left(5 + frac{1000000}{x}right) left(frac{x}{1000} + 15right) + 200 + frac{10000000}{x}}$$
((10/(-1/4) + 1/1500)*(5 + 1000000/(-1/4)))/((15 + (-1/4)/1000)*(5 + 1000000/(-1/4)) + 200 + (-1/4)/100 + 10000000/(-1/4))
$$frac{left(frac{1}{1500} + frac{10}{(-1/4)}right) left(5 + frac{1000000}{(-1/4)}right)}{frac{(-1/4)}{100} + left(5 + frac{1000000}{(-1/4)}right) left(frac{(-1/4)}{1000} + 15right) + 200 + frac{10000000}{(-1/4)}}$$
((10/(-1/4) + 1/1500)*(5 + 1000000/(-1/4)))/((15 – 1/4000)*(5 + 1000000/(-1/4)) + 200 – 1/400 + 10000000/(-1/4))
$$frac{left(frac{10}{- frac{1}{4}} + frac{1}{1500}right) left(frac{1000000}{- frac{1}{4}} + 5right)}{left(frac{1000000}{- frac{1}{4}} + 5right) left(- frac{1}{4000} + 15right) + 200 – frac{1}{400} + frac{10000000}{- frac{1}{4}}}$$
-383993120008/239996940009
$$- frac{383993120008}{239996940009}$$
Численный ответ
(5.0 + 1000000.0/x)*(0.000666666666666667 + 10.0/x)/(200.0 + 10000000.0/x + 0.01*x + (5.0 + 1000000.0/x)*(15.0 + 0.001*x))
Рациональный знаменатель
$$frac{2 x^{2} + 430000 x + 6000000000}{3 x left(3 x^{2} + 255000 x + 5000000000right)}$$
Объединение рациональных выражений
$$frac{2 left(x + 15000right) left(x + 200000right)}{3 x left(2 x^{2} + 40000 x + left(x + 15000right) left(x + 200000right) + 2000000000right)}$$
Общее упрощение
/ 2
2*3000000000 + x + 215000*x/
———————————-
/ 2
3*x*5000000000 + 3*x + 255000*x/
$$frac{2 x^{2} + 430000 x + 6000000000}{3 x left(3 x^{2} + 255000 x + 5000000000right)}$$
Общий знаменатель
2
6000000000 + 2*x + 430000*x
——————————–
3 2
9*x + 765000*x + 15000000000*x
$$frac{2 x^{2} + 430000 x + 6000000000}{9 x^{3} + 765000 x^{2} + 15000000000 x}$$
Комбинаторика
2*(15000 + x)*(200000 + x)
———————————-
/ 2
3*x*5000000000 + 3*x + 255000*x/
$$frac{2 left(x + 15000right) left(x + 200000right)}{3 x left(3 x^{2} + 255000 x + 5000000000right)}$$
