Descomposición de una fracción
[src]
sqrt(2025/(100*w^2 + 81) - 40000*w^6/(100*w^2 + 81) - 15824*w^4/(100*w^2 + 81) + 3600*w^2/(100*w^2 + 81) + 52800*w^5/(100*w^2 + 81))
$$\sqrt{- \frac{40000 w^{6}}{100 w^{2} + 81} + \frac{52800 w^{5}}{100 w^{2} + 81} - \frac{15824 w^{4}}{100 w^{2} + 81} + \frac{3600 w^{2}}{100 w^{2} + 81} + \frac{2025}{100 w^{2} + 81}}$$
_____________________________________________________________________
/ 6 4 2 5
/ 2025 40000*w 15824*w 3600*w 52800*w
/ ----------- - ----------- - ----------- + ----------- + -----------
/ 2 2 2 2 2
\/ 100*w + 81 100*w + 81 100*w + 81 100*w + 81 100*w + 81
Simplificación general
[src]
______________________________________
/ 2
/ / 2\ 4 2
/ 25*\9 + 8*w / - 16*w *(-33 + 50*w)
/ ------------------------------------
/ 2
\/ 81 + 100*w
$$\sqrt{\frac{- 16 w^{4} \left(50 w - 33\right)^{2} + 25 \left(8 w^{2} + 9\right)^{2}}{100 w^{2} + 81}}$$
sqrt((25*(9 + 8*w^2)^2 - 16*w^4*(-33 + 50*w)^2)/(81 + 100*w^2))
Compilar la expresión
[src]
______________________________________
/ 2 2
/ / 2\ / 2 3\
/ \45 + 40*w / \- 132*w + 200*w /
/ ------------- - --------------------
/ 2 2
\/ 81 + 100*w 81 + 100*w
$$\sqrt{\frac{\left(40 w^{2} + 45\right)^{2}}{100 w^{2} + 81} - \frac{\left(200 w^{3} - 132 w^{2}\right)^{2}}{100 w^{2} + 81}}$$
sqrt((45 + 40*w^2)^2/(81 + 100*w^2) - (-132*w^2 + 200*w^3)^2/(81 + 100*w^2))
Denominador racional
[src]
__________________________________________
/ 2 2
/ / 2 3\ / 2\
/ - 16*\- 33*w + 50*w / + 25*\9 + 8*w /
/ ----------------------------------------
/ 2
\/ 100*w + 81
$$\sqrt{\frac{25 \left(8 w^{2} + 9\right)^{2} - 16 \left(50 w^{3} - 33 w^{2}\right)^{2}}{100 w^{2} + 81}}$$
sqrt((-16*(-33*w^2 + 50*w^3)^2 + 25*(9 + 8*w^2)^2)/(100*w^2 + 81))
200.0*(-(w^3 - 0.66*w^2)^2/(81.0 + 100.0*w^2) + 0.050625*(1 + 0.888888888888889*w^2)^2/(81.0 + 100.0*w^2))^0.5
200.0*(-(w^3 - 0.66*w^2)^2/(81.0 + 100.0*w^2) + 0.050625*(1 + 0.888888888888889*w^2)^2/(81.0 + 100.0*w^2))^0.5
______________________________________
/ 2 2
/ / 2\ / 2 3\
/ \45 + 40*w / \- 132*w + 200*w /
/ ------------- - --------------------
/ 2 2
\/ 81 + 100*w 81 + 100*w
$$\sqrt{\frac{\left(40 w^{2} + 45\right)^{2}}{100 w^{2} + 81} - \frac{\left(200 w^{3} - 132 w^{2}\right)^{2}}{100 w^{2} + 81}}$$
sqrt((45 + 40*w^2)^2/(81 + 100*w^2) - (-132*w^2 + 200*w^3)^2/(81 + 100*w^2))
_____________________________________________________________________
/ 6 4 2 5
/ 2025 40000*w 15824*w 3600*w 52800*w
/ ----------- - ----------- - ----------- + ----------- + -----------
/ 2 2 2 2 2
\/ 81 + 100*w 81 + 100*w 81 + 100*w 81 + 100*w 81 + 100*w
$$\sqrt{- \frac{40000 w^{6}}{100 w^{2} + 81} + \frac{52800 w^{5}}{100 w^{2} + 81} - \frac{15824 w^{4}}{100 w^{2} + 81} + \frac{3600 w^{2}}{100 w^{2} + 81} + \frac{2025}{100 w^{2} + 81}}$$
sqrt(2025/(81 + 100*w^2) - 40000*w^6/(81 + 100*w^2) - 15824*w^4/(81 + 100*w^2) + 3600*w^2/(81 + 100*w^2) + 52800*w^5/(81 + 100*w^2))
Parte trigonométrica
[src]
______________________________________
/ 2 2
/ / 2\ / 2 3\
/ \45 + 40*w / \- 132*w + 200*w /
/ ------------- - --------------------
/ 2 2
\/ 81 + 100*w 81 + 100*w
$$\sqrt{\frac{\left(40 w^{2} + 45\right)^{2}}{100 w^{2} + 81} - \frac{\left(200 w^{3} - 132 w^{2}\right)^{2}}{100 w^{2} + 81}}$$
sqrt((45 + 40*w^2)^2/(81 + 100*w^2) - (-132*w^2 + 200*w^3)^2/(81 + 100*w^2))
_________________________________________________
/ / 2 3\ / 2 3\
/ -\-45 - 172*w + 200*w /*\45 - 92*w + 200*w /
/ -----------------------------------------------
/ 2
\/ 81 + 100*w
$$\sqrt{- \frac{\left(200 w^{3} - 172 w^{2} - 45\right) \left(200 w^{3} - 92 w^{2} + 45\right)}{100 w^{2} + 81}}$$
sqrt(-(-45 - 172*w^2 + 200*w^3)*(45 - 92*w^2 + 200*w^3)/(81 + 100*w^2))
Unión de expresiones racionales
[src]
______________________________________
/ 2
/ / 2\ 4 2
/ 25*\9 + 8*w / - 16*w *(-33 + 50*w)
/ ------------------------------------
/ 2
\/ 81 + 100*w
$$\sqrt{\frac{- 16 w^{4} \left(50 w - 33\right)^{2} + 25 \left(8 w^{2} + 9\right)^{2}}{100 w^{2} + 81}}$$
sqrt((25*(9 + 8*w^2)^2 - 16*w^4*(-33 + 50*w)^2)/(81 + 100*w^2))