(40+40*1/(150*p^2+25*p+1))*1/(1+40*1/((1+10*p)^2*(1+15*p))) если p=-1/4 (упростите выражение)

$$frac{40 + frac{40}{150 p^{2} + 25 p + 1}}{1 + frac{40}{left(10 p + 1right)^{2} left(15 p + 1right)}}$$

$$frac{40 + frac{40}{150 p^{2} + 25 p + 1}}{1 + frac{40}{left(10 p + 1right)^{2} left(15 p + 1right)}}$$

(40 + 40/(150*(-1/4)^2 + 25*(-1/4) + 1))/(1 + 40/((1 + 10*(-1/4))^2*(1 + 15*(-1/4))))

$$frac{40 + frac{40}{150 (-1/4)^{2} + 25 (-1/4) + 1}}{1 + frac{40}{left(10 (-1/4) + 1right)^{2} left(15 (-1/4) + 1right)}}$$

(40 + 40/(150*(-1/4)^2 + 25*(-1)/4 + 1))/(1 + 40/((1 + 10*(-1)/4)^2*(1 + 15*(-1)/4)))

$$frac{frac{40}{1 + frac{-25}{4} + 150 left(- frac{1}{4}right)^{2}} + 40}{frac{40}{left(frac{-10}{4} + 1right)^{2} left(frac{-15}{4} + 1right)} + 1}$$

-4920/541

$$- frac{4920}{541}$$

(40.0 + 40.0/(1.0 + 25.0*p + 150.0*p^2))/(1.0 + 40.0/((1.0 + 10.0*p)^2*(1.0 + 15.0*p)))

$$frac{90000 p^{3} left(10 p + 1right)^{2} + 21000 p^{2} left(10 p + 1right)^{2} + 2200 p left(10 p + 1right)^{2} + 80 left(10 p + 1right)^{2}}{left(150 p^{2} + 25 p + 1right) left(1500 p^{3} + 400 p^{2} + 35 p + 41right)}$$

$$frac{40 left(10 p + 1right)^{2} left(15 p + 1right) left(25 p left(6 p + 1right) + 2right)}{left(25 p left(6 p + 1right) + 1right) left(left(10 p + 1right)^{2} left(15 p + 1right) + 40right)}$$

/ 2 3
40*2 + 45*p + 400*p + 1500*p /
——————————–
2 3
41 + 35*p + 400*p + 1500*p

$$frac{60000 p^{3} + 16000 p^{2} + 1800 p + 80}{1500 p^{3} + 400 p^{2} + 35 p + 41}$$

-1560 + 400*p
40 + —————————-
2 3
41 + 35*p + 400*p + 1500*p

$$frac{400 p – 1560}{1500 p^{3} + 400 p^{2} + 35 p + 41} + 40$$

/ 2
40*(1 + 10*p)*2 + 25*p + 150*p /
———————————
2 3
41 + 35*p + 400*p + 1500*p

$$frac{40 left(10 p + 1right) left(150 p^{2} + 25 p + 2right)}{1500 p^{3} + 400 p^{2} + 35 p + 41}$$