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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 --------- + - ---------- + 3 ___ ___ \/ 8 + 2 \/ 8
$$\frac{\sqrt{2}}{2 + \sqrt{8}} + \left(- \frac{6 - \sqrt{32}}{\sqrt{8}} + 3\right)$$
sqrt(2)/(sqrt(8) + 2) - (6 - sqrt(32))/sqrt(8) + 3
Parte trigonométrica
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___ ___ / ___\
\/ 2 \/ 2 *\6 - 4*\/ 2 /
3 + ----------- - -------------------
___ 4
2 + 2*\/ 2
$$- \frac{\sqrt{2} \left(6 - 4 \sqrt{2}\right)}{4} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}} + 3$$
3 + sqrt(2)/(2 + 2*sqrt(2)) - sqrt(2)*(6 - 4*sqrt(2))/4
Denominador común
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2
4 - ---------
___
1 + \/ 2
$$4 - \frac{2}{1 + \sqrt{2}}$$
4 - 2/(1 + sqrt(2))
Potencias
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___
\/ 2 ___ / 3 ___\
3 + ----------- + \/ 2 *|- - + \/ 2 |
___ \ 2 /
2 + 2*\/ 2
$$\sqrt{2} \left(- \frac{3}{2} + \sqrt{2}\right) + \frac{\sqrt{2}}{2 + 2 \sqrt{2}} + 3$$
___ ___ / ___\
\/ 2 \/ 2 *\6 - 4*\/ 2 /
3 + ----------- - -------------------
___ 4
2 + 2*\/ 2
$$- \frac{\sqrt{2} \left(6 - 4 \sqrt{2}\right)}{4} + \frac{\sqrt{2}}{2 + 2 \sqrt{2}} + 3$$
3 + sqrt(2)/(2 + 2*sqrt(2)) - sqrt(2)*(6 - 4*sqrt(2))/4
Unión de expresiones racionales
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___ / ___\ / ___ / ___\\
\/ 2 + \1 + \/ 2 /*\6 - \/ 2 *\3 - 2*\/ 2 //
---------------------------------------------
/ ___\
2*\1 + \/ 2 /
$$\frac{\sqrt{2} + \left(1 + \sqrt{2}\right) \left(- \sqrt{2} \left(3 - 2 \sqrt{2}\right) + 6\right)}{2 \left(1 + \sqrt{2}\right)}$$
(sqrt(2) + (1 + sqrt(2))*(6 - sqrt(2)*(3 - 2*sqrt(2))))/(2*(1 + sqrt(2)))
Combinatoria
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/ ___\
2*\1 + 2*\/ 2 /
---------------
___
1 + \/ 2
$$\frac{2 \left(1 + 2 \sqrt{2}\right)}{1 + \sqrt{2}}$$
2*(1 + 2*sqrt(2))/(1 + sqrt(2))