24*1/(4111/500)*1/((s+959/500)*(s-69/1000)*(s-459/500))*e^(-3*s)/25 если s=1/2 (упростите выражение)

$$frac{1}{25} frac{12000}{4111} frac{1}{left(s – frac{459}{500}right) left(s – frac{69}{1000}right) left(s + frac{959}{500}right)} e^{- 3 s}$$

$$frac{1}{25} frac{12000}{4111} frac{1}{left(s – frac{459}{500}right) left(s – frac{69}{1000}right) left(s + frac{959}{500}right)} e^{- 3 s}$$

(((24/(4111/500))/((((1/2) + 959/500)*((1/2) – 69/1000))*((1/2) – 459/500)))*E^(-3*(1/2)))/25

$$frac{1}{25} frac{12000}{4111} frac{1}{left((1/2) – frac{459}{500}right) left((1/2) – frac{69}{1000}right) left((1/2) + frac{959}{500}right)} e^{- 3 (1/2)}$$

(((24/(4111/500))/(((1/2 + 959/500)*(1/2 – 69/1000))*(1/2 – 459/500)))*E^(-3/2))/25

$$frac{e^{- frac{3}{2}}}{25} frac{24}{frac{4111}{500}} frac{1}{left(- frac{69}{1000} + frac{1}{2}right) left(frac{1}{2} + frac{959}{500}right) left(- frac{459}{500} + frac{1}{2}right)}$$

-40000000000*exp(-3/2)/149236851907

$$- frac{40000000000}{149236851907 e^{frac{3}{2}}}$$

$$frac{480 e^{- 3 s}}{4111 left(s – frac{459}{500}right) left(s – frac{69}{1000}right) left(s + frac{959}{500}right)}$$

0.116759912430066*2.71828182845905^(-3.0*s)/((1.918 + s)*(-0.069 + s)*(-0.918 + s))

$$frac{120000000000 e^{- 3 s}}{4111 left(500 s – 459right) left(500 s + 959right) left(1000 s – 69right)}$$

$$frac{120000000000 e^{- 3 s}}{4111 left(500 s – 459right) left(500 s + 959right) left(1000 s – 69right)}$$

-3*s
120000000000*e
————————————————
4111*(-459 + 500*s)*(-69 + 1000*s)*(959 + 500*s)

$$frac{120000000000 e^{- 3 s}}{4111 left(500 s – 459right) left(500 s + 959right) left(1000 s – 69right)}$$

$$frac{480 e^{- 3 s}}{4111 left(s – frac{459}{500}right) left(s – frac{69}{1000}right) left(s + frac{959}{500}right)}$$

120000000000
—————————————————————————————
3*s 3*s 2 3*s 3 3*s
124861302279*e – 1880498841000*s*e + 956835250000*s *e + 1027750000000*s *e

$$frac{120000000000}{1027750000000 s^{3} e^{3 s} + 956835250000 s^{2} e^{3 s} – 1880498841000 s e^{3 s} + 124861302279 e^{3 s}}$$

-3*s
120000000000*e
————————————————
4111*(-459 + 500*s)*(-69 + 1000*s)*(959 + 500*s)

$$frac{120000000000 e^{- 3 s}}{4111 left(500 s – 459right) left(500 s + 959right) left(1000 s – 69right)}$$

-3*s
480*e
———————————–
/ 459 / 69 / 959
4111*|s – —|*|s – —-|*|s + —|
500/ 1000/ 500/

$$frac{480 e^{- 3 s}}{4111 left(s – frac{459}{500}right) left(s – frac{69}{1000}right) left(s + frac{959}{500}right)}$$