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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(2)*(4-3*(1+x-2*x^2)/(1+2*x)^2-2*(-1+4*x)/(1+2*x))/(6*sqrt(1+2*x))

¿Cómo vas a descomponer esta sqrt(2)*(4-3*(1+x-2*x^2)/(1+2*x)^2-2*(-1+4*x)/(1+2*x))/(6*sqrt(1+2*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      /      /           2\               \
  ___ |    3*\1 + x - 2*x /   2*(-1 + 4*x)|
\/ 2 *|4 - ---------------- - ------------|
      |                2        1 + 2*x   |
      \       (1 + 2*x)                   /
-------------------------------------------
                   _________               
               6*\/ 1 + 2*x
2((4−3(−2x2+(x+1))(2x+1)2)−2(4x−1)2x+1)62x+1\frac{\sqrt{2} \left(\left(4 - \frac{3 \left(- 2 x^{2} + \left(x + 1\right)\right)}{\left(2 x + 1\right)^{2}}\right) - \frac{2 \left(4 x - 1\right)}{2 x + 1}\right)}{6 \sqrt{2 x + 1}} 
(sqrt(2)*(4 - 3*(1 + x - 2*x^2)/(1 + 2*x)^2 - 2*(-1 + 4*x)/(1 + 2*x)))/((6*sqrt(1 + 2*x)))
Simplificación general [src] 
  ___         
\/ 2 *(1 + x) 
--------------
           3/2
2*(1 + 2*x)
2(x+1)2(2x+1)32\frac{\sqrt{2} \left(x + 1\right)}{2 \left(2 x + 1\right)^{\frac{3}{2}}} 
sqrt(2)*(1 + x)/(2*(1 + 2*x)^(3/2))
Respuesta numérica [src] 
0.117851130197758*(0.5 + x)^(-0.5)*(5.65685424949238 - 0.353553390593274*(3.0 + 3.0*x - 6.0*x^2)/(0.5 + x)^2 - 1.4142135623731*(-2.0 + 8.0*x)/(1.0 + 2.0*x))
0.117851130197758*(0.5 + x)^(-0.5)*(5.65685424949238 - 0.353553390593274*(3.0 + 3.0*x - 6.0*x^2)/(0.5 + x)^2 - 1.4142135623731*(-2.0 + 8.0*x)/(1.0 + 2.0*x))
Parte trigonométrica [src] 
      /                      2      \
  ___ |    -2 + 8*x   3 - 6*x  + 3*x|
\/ 2 *|4 - -------- - --------------|
      |    1 + 2*x               2  |
      \                 (1 + 2*x)   /
-------------------------------------
                _________            
            6*\/ 1 + 2*x
2(4−8x−22x+1−−6x2+3x+3(2x+1)2)62x+1\frac{\sqrt{2} \left(4 - \frac{8 x - 2}{2 x + 1} - \frac{- 6 x^{2} + 3 x + 3}{\left(2 x + 1\right)^{2}}\right)}{6 \sqrt{2 x + 1}} 
sqrt(2)*(4 - (-2 + 8*x)/(1 + 2*x) - (3 - 6*x^2 + 3*x)/(1 + 2*x)^2)/(6*sqrt(1 + 2*x))
Denominador racional [src] 
  ___   _________ /                      2      3\
\/ 2 *\/ 1 + 2*x *\-1 - 3*x + 2*(1 + 2*x)  + 4*x /
--------------------------------------------------
                        4       2       3         
         2 + 16*x + 32*x  + 48*x  + 64*x
22x+1(4x3−3x+2(2x+1)2−1)32x4+64x3+48x2+16x+2\frac{\sqrt{2} \sqrt{2 x + 1} \left(4 x^{3} - 3 x + 2 \left(2 x + 1\right)^{2} - 1\right)}{32 x^{4} + 64 x^{3} + 48 x^{2} + 16 x + 2} 
sqrt(2)*sqrt(1 + 2*x)*(-1 - 3*x + 2*(1 + 2*x)^2 + 4*x^3)/(2 + 16*x + 32*x^4 + 48*x^2 + 64*x^3)
Compilar la expresión [src] 
      /                      2      \
  ___ |    -2 + 8*x   3 - 6*x  + 3*x|
\/ 2 *|4 - -------- - --------------|
      |    1 + 2*x               2  |
      \                 (1 + 2*x)   /
-------------------------------------
                _________            
            6*\/ 1 + 2*x
2(4−8x−22x+1−−6x2+3x+3(2x+1)2)62x+1\frac{\sqrt{2} \left(4 - \frac{8 x - 2}{2 x + 1} - \frac{- 6 x^{2} + 3 x + 3}{\left(2 x + 1\right)^{2}}\right)}{6 \sqrt{2 x + 1}} 
sqrt(2)*(4 - (-2 + 8*x)/(1 + 2*x) - (3 - 6*x^2 + 3*x)/(1 + 2*x)^2)/(6*sqrt(1 + 2*x))
Potencias [src] 
      /                      2      \
  ___ |    -2 + 8*x   3 - 6*x  + 3*x|
\/ 2 *|4 - -------- - --------------|
      |    1 + 2*x               2  |
      \                 (1 + 2*x)   /
-------------------------------------
                _________            
            6*\/ 1 + 2*x
2(4−8x−22x+1−−6x2+3x+3(2x+1)2)62x+1\frac{\sqrt{2} \left(4 - \frac{8 x - 2}{2 x + 1} - \frac{- 6 x^{2} + 3 x + 3}{\left(2 x + 1\right)^{2}}\right)}{6 \sqrt{2 x + 1}} 
      /                                2\
  ___ |2     2 - 8*x     -3 - 3*x + 6*x |
\/ 2 *|- + ----------- + ---------------|
      |3   6*(1 + 2*x)                2 |
      \                    6*(1 + 2*x)  /
-----------------------------------------
                 _________               
               \/ 1 + 2*x
2(2−8x6(2x+1)+23+6x2−3x−36(2x+1)2)2x+1\frac{\sqrt{2} \left(\frac{2 - 8 x}{6 \left(2 x + 1\right)} + \frac{2}{3} + \frac{6 x^{2} - 3 x - 3}{6 \left(2 x + 1\right)^{2}}\right)}{\sqrt{2 x + 1}} 
sqrt(2)*(2/3 + (2 - 8*x)/(6*(1 + 2*x)) + (-3 - 3*x + 6*x^2)/(6*(1 + 2*x)^2))/sqrt(1 + 2*x)
Unión de expresiones racionales [src] 
  ___ /                      2      2                         \
\/ 2 *\-3 - 3*x + 4*(1 + 2*x)  + 6*x  - 2*(1 + 2*x)*(-1 + 4*x)/
---------------------------------------------------------------
                                    5/2                        
                         6*(1 + 2*x)
2(6x2−3x+4(2x+1)2−2(2x+1)(4x−1)−3)6(2x+1)52\frac{\sqrt{2} \left(6 x^{2} - 3 x + 4 \left(2 x + 1\right)^{2} - 2 \left(2 x + 1\right) \left(4 x - 1\right) - 3\right)}{6 \left(2 x + 1\right)^{\frac{5}{2}}} 
sqrt(2)*(-3 - 3*x + 4*(1 + 2*x)^2 + 6*x^2 - 2*(1 + 2*x)*(-1 + 4*x))/(6*(1 + 2*x)^(5/2))
Combinatoria [src] 
  ___         
\/ 2 *(1 + x) 
--------------
           3/2
2*(1 + 2*x)
2(x+1)2(2x+1)32\frac{\sqrt{2} \left(x + 1\right)}{2 \left(2 x + 1\right)^{\frac{3}{2}}} 
sqrt(2)*(1 + x)/(2*(1 + 2*x)^(3/2))
Denominador común [src] 
          ___       ___        
        \/ 2  + x*\/ 2         
-------------------------------
    _________         _________
2*\/ 1 + 2*x  + 4*x*\/ 1 + 2*x
2x+24x2x+1+22x+1\frac{\sqrt{2} x + \sqrt{2}}{4 x \sqrt{2 x + 1} + 2 \sqrt{2 x + 1}} 
(sqrt(2) + x*sqrt(2))/(2*sqrt(1 + 2*x) + 4*x*sqrt(1 + 2*x))
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