Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)
¿Cómo vas a descomponer esta sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2) expresión en fracciones?
Solución
Ha introducido
[src]
_____________________________
/ 2
/ / 2 / 2\\ 2
/ | w *\-t /| / t*w \
/ |---------| + |---------|
/ | 2 2| | 2 2|
\/ \1 + t *w / \1 + t *w /
$$\sqrt{\left(\frac{t w}{t^{2} w^{2} + 1}\right)^{2} + \left(\frac{- t^{2} w^{2}}{t^{2} w^{2} + 1}\right)^{2}}$$
sqrt(((w^2*(-t^2))/(1 + t^2*w^2))^2 + ((t*w)/(1 + t^2*w^2))^2)
Descomposición de una fracción
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sqrt(t^2*w^2/(1 + t^4*w^4 + 2*t^2*w^2) + t^4*w^4/(1 + t^4*w^4 + 2*t^2*w^2))
$$\sqrt{\frac{t^{4} w^{4}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1} + \frac{t^{2} w^{2}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1}}$$
___________________________________________
/ 2 2 4 4
/ t *w t *w
/ ------------------- + -------------------
/ 4 4 2 2 4 4 2 2
\/ 1 + t *w + 2*t *w 1 + t *w + 2*t *w
Simplificación general
[src]
___________
/ 2 2
/ t *w
/ ---------
/ 2 2
\/ 1 + t *w
$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$
sqrt(t^2*w^2/(1 + t^2*w^2))
Respuesta numérica
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(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5
(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5
Parte trigonométrica
[src]
_____________________________
/ 2 2 4 4
/ t *w t *w
/ ------------ + ------------
/ 2 2
/ / 2 2\ / 2 2\
\/ \1 + t *w / \1 + t *w /
$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Potencias
[src]
_____________________________
/ 2 2 4 4
/ t *w t *w
/ ------------ + ------------
/ 2 2
/ / 2 2\ / 2 2\
\/ \1 + t *w / \1 + t *w /
$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Combinatoria
[src]
___________
/ 2 2
/ t *w
/ ---------
/ 2 2
\/ 1 + t *w
$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$
sqrt(t^2*w^2/(1 + t^2*w^2))
Unión de expresiones racionales
[src]
___________
/ 2 2
/ t *w
/ ---------
/ 2 2
\/ 1 + t *w
$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$
sqrt(t^2*w^2/(1 + t^2*w^2))
Compilar la expresión
[src]
_____________________________
/ 2 2 4 4
/ t *w t *w
/ ------------ + ------------
/ 2 2
/ / 2 2\ / 2 2\
\/ \1 + t *w / \1 + t *w /
$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Denominador racional
[src]
___________
/ 2 2
/ t *w
/ ---------
/ 2 2
\/ 1 + t *w
$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$
sqrt(t^2*w^2/(1 + t^2*w^2))
Denominador común
[src]
___________
/ 2 2
/ t *w
/ ---------
/ 2 2
\/ 1 + t *w
$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$
sqrt(t^2*w^2/(1 + t^2*w^2))