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