Дано
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} + frac{- sqrt{3} + 2}{- sqrt{- 9 r t + 2} + sqrt{2}}$$
Подстановка условия
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} + frac{- sqrt{3} + 2}{- sqrt{- 9 r t + 2} + sqrt{2}}$$
(2 + sqrt(3))/(sqrt(2) + sqrt(2 + sqrt(3))) + (2 – sqrt(3))/(sqrt(2) – sqrt(2 – (-2)*t*9))
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} + frac{- sqrt{3} + 2}{- sqrt{- 9 (-2) t + 2} + sqrt{2}}$$
(2 + sqrt(3))/(sqrt(2) + sqrt(2 + sqrt(3))) + (2 – sqrt(3))/(sqrt(2) – sqrt(2 – (-2*t)*9))
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} + frac{- sqrt{3} + 2}{- sqrt{- -1 cdot 18 t + 2} + sqrt{2}}$$
(2 + sqrt(3))/(sqrt(2) + sqrt(2 + sqrt(3))) + (2 – sqrt(3))/(sqrt(2) – sqrt(2 + 18*t))
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} + frac{- sqrt{3} + 2}{- sqrt{18 t + 2} + sqrt{2}}$$
Численный ответ
1.11535507165041 + 0.267949192431123/(1.4142135623731 – (2.0 – 9.0*r*t)^0.5)
Рациональный знаменатель
$$frac{1}{27 r t} left(- 18 sqrt{6} r t – 27 sqrt{2} r t + 27 r t sqrt{sqrt{3} + 2} + 18 sqrt{3} r t sqrt{sqrt{3} + 2} – 3 sqrt{3} sqrt{- 9 r t + 2} + 6 sqrt{- 9 r t + 2} – 3 sqrt{6} + 6 sqrt{2}right)$$
Объединение рациональных выражений
$$frac{left(sqrt{3} + 2right) left(- sqrt{- 9 r t + 2} + sqrt{2}right) + left(sqrt{2} + sqrt{sqrt{3} + 2}right) left(- sqrt{3} + 2right)}{left(sqrt{2} + sqrt{sqrt{3} + 2}right) left(- sqrt{- 9 r t + 2} + sqrt{2}right)}$$
Общее упрощение
___ ___
2 + / 3 2 – / 3
———————- – ———————
___________ ___________ ___
___ / ___ / 2 – 9*r*t – / 2
/ 2 + / 2 + / 3
$$frac{sqrt{3} + 2}{sqrt{2} + sqrt{sqrt{3} + 2}} – frac{- sqrt{3} + 2}{sqrt{- 9 r t + 2} – sqrt{2}}$$
Общий знаменатель
___________ ___________
___ / ___ ___________ ___ / ___ ___ ___________
– 4*/ 2 – 2*/ 2 + / 3 + 2*/ 2 – 9*r*t + / 3 */ 2 + / 3 + / 3 */ 2 – 9*r*t
——————————————————————————————-
___________ ___________
___ ___________ / ___ ___________ ___ / ___
-2 + / 2 */ 2 – 9*r*t + / 2 + / 3 */ 2 – 9*r*t – / 2 */ 2 + / 3
$$frac{sqrt{3} sqrt{- 9 r t + 2} + 2 sqrt{- 9 r t + 2} – 4 sqrt{2} – 2 sqrt{sqrt{3} + 2} + sqrt{3} sqrt{sqrt{3} + 2}}{sqrt{2} sqrt{- 9 r t + 2} + sqrt{sqrt{3} + 2} sqrt{- 9 r t + 2} – sqrt{2} sqrt{sqrt{3} + 2} – 2}$$
Комбинаторика
___________ ___________
___ / ___ ___________ ___ / ___ ___ ___________
– 4*/ 2 – 2*/ 2 + / 3 + 2*/ 2 – 9*r*t + / 3 */ 2 + / 3 + / 3 */ 2 – 9*r*t
——————————————————————————————-
/ ___________
| ___ / ___ | / ___________ ___
/ 2 + / 2 + / 3 /*/ 2 – 9*r*t – / 2 /
$$frac{1}{left(sqrt{2} + sqrt{sqrt{3} + 2}right) left(sqrt{- 9 r t + 2} – sqrt{2}right)} left(sqrt{3} sqrt{- 9 r t + 2} + 2 sqrt{- 9 r t + 2} – 4 sqrt{2} – 2 sqrt{sqrt{3} + 2} + sqrt{3} sqrt{sqrt{3} + 2}right)$$