Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(2)/(sqrt(8)+2)-(6-sqrt(32))/sqrt((8)-3)
¿Cómo vas a descomponer esta sqrt(2)/(sqrt(8)+2)-(6-sqrt(32))/sqrt((8)-3) expresión en fracciones?
Solución
Ha introducido
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___ ____ \/ 2 6 - \/ 32 --------- - ---------- ___ ___ \/ 8 + 2 \/ 5
$$- \frac{6 - \sqrt{32}}{\sqrt{5}} + \frac{\sqrt{2}}{2 + \sqrt{8}}$$
sqrt(2)/(sqrt(8) + 2) - (6 - sqrt(32))/sqrt(5)
Simplificación general
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___ ___ ____
6*\/ 5 \/ 2 4*\/ 10
1 - ------- - ----- + --------
5 2 5
$$- \frac{6 \sqrt{5}}{5} - \frac{\sqrt{2}}{2} + 1 + \frac{4 \sqrt{10}}{5}$$
1 - 6*sqrt(5)/5 - sqrt(2)/2 + 4*sqrt(10)/5
Potencias
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___ / ___\
\/ 2 ___ | 6 4*\/ 2 |
----------- + \/ 5 *|- - + -------|
___ \ 5 5 /
2 + 2*\/ 2
$$\sqrt{5} \left(- \frac{6}{5} + \frac{4 \sqrt{2}}{5}\right) + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$
___ ___ / ___\
\/ 2 \/ 5 *\6 - 4*\/ 2 /
----------- - -------------------
___ 5
2 + 2*\/ 2
$$- \frac{\sqrt{5} \left(6 - 4 \sqrt{2}\right)}{5} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$
sqrt(2)/(2 + 2*sqrt(2)) - sqrt(5)*(6 - 4*sqrt(2))/5
Denominador racional
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___ ___ ____
10 - 12*\/ 5 - 5*\/ 2 + 8*\/ 10
----------------------------------
10
$$\frac{- 12 \sqrt{5} - 5 \sqrt{2} + 10 + 8 \sqrt{10}}{10}$$
(10 - 12*sqrt(5) - 5*sqrt(2) + 8*sqrt(10))/10
Combinatoria
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/ ___ ___ ____\
-\- 5*\/ 2 - 4*\/ 5 + 4*\/ 10 /
----------------------------------
/ ___\
10*\1 + \/ 2 /
$$- \frac{- 4 \sqrt{5} - 5 \sqrt{2} + 4 \sqrt{10}}{10 \left(1 + \sqrt{2}\right)}$$
-(-5*sqrt(2) - 4*sqrt(5) + 4*sqrt(10))/(10*(1 + sqrt(2)))
Unión de expresiones racionales
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___ ___ / ___\ / ___\
5*\/ 2 - 4*\/ 5 *\1 + \/ 2 /*\3 - 2*\/ 2 /
-------------------------------------------
/ ___\
10*\1 + \/ 2 /
$$\frac{- 4 \sqrt{5} \left(1 + \sqrt{2}\right) \left(3 - 2 \sqrt{2}\right) + 5 \sqrt{2}}{10 \left(1 + \sqrt{2}\right)}$$
(5*sqrt(2) - 4*sqrt(5)*(1 + sqrt(2))*(3 - 2*sqrt(2)))/(10*(1 + sqrt(2)))
Parte trigonométrica
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___ ___ / ___\
\/ 2 \/ 5 *\6 - 4*\/ 2 /
----------- - -------------------
___ 5
2 + 2*\/ 2
$$- \frac{\sqrt{5} \left(6 - 4 \sqrt{2}\right)}{5} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}}$$
sqrt(2)/(2 + 2*sqrt(2)) - sqrt(5)*(6 - 4*sqrt(2))/5
Denominador común
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___ ____
1 5 - 4*\/ 5 + 4*\/ 10
- - ----------------------
2 ___
10 + 10*\/ 2
$$- \frac{- 4 \sqrt{5} + 5 + 4 \sqrt{10}}{10 + 10 \sqrt{2}} + \frac{1}{2}$$
1/2 - (5 - 4*sqrt(5) + 4*sqrt(10))/(10 + 10*sqrt(2))