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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(8*x-x*x-7)/2+(4-x)*(x-4)/(2*sqrt(8*x-x*x-7))+3*sqrt(6)/(4*sqrt(7/6-x/6)*sqrt(x-1))

¿Cómo vas a descomponer esta sqrt(8*x-x*x-7)/2+(4-x)*(x-4)/(2*sqrt(8*x-x*x-7))+3*sqrt(6)/(4*sqrt(7/6-x/6)*sqrt(x-1)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  _______________                                     ___        
\/ 8*x - x*x - 7      (4 - x)*(x - 4)             3*\/ 6         
----------------- + ------------------- + -----------------------
        2               _______________         _______          
                    2*\/ 8*x - x*x - 7         / 7   x    _______
                                          4*  /  - - - *\/ x - 1 
                                            \/   6   6
((4−x)(x−4)2(−xx+8x)−7+(−xx+8x)−72)+36x−1⋅4−x6+76\left(\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{\left(- x x + 8 x\right) - 7}} + \frac{\sqrt{\left(- x x + 8 x\right) - 7}}{2}\right) + \frac{3 \sqrt{6}}{\sqrt{x - 1} \cdot 4 \sqrt{- \frac{x}{6} + \frac{7}{6}}} 
sqrt(8*x - x*x - 7)/2 + ((4 - x)*(x - 4))/((2*sqrt(8*x - x*x - 7))) + (3*sqrt(6))/(((4*sqrt(7/6 - x/6))*sqrt(x - 1)))
Simplificación general [src] 
     _______________                                                                        
    /       2            ________   _______ /      2      \     ________         2   _______
9*\/  -7 - x  + 8*x  + \/ -1 + x *\/ 7 - x *\-7 - x  + 8*x/ - \/ -1 + x *(-4 + x) *\/ 7 - x 
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                                                   _______________                          
                             ________   _______   /       2                                 
                         2*\/ -1 + x *\/ 7 - x *\/  -7 - x  + 8*x
−7−x(x−4)2x−1+7−xx−1(−x2+8x−7)+9−x2+8x−727−xx−1−x2+8x−7\frac{- \sqrt{7 - x} \left(x - 4\right)^{2} \sqrt{x - 1} + \sqrt{7 - x} \sqrt{x - 1} \left(- x^{2} + 8 x - 7\right) + 9 \sqrt{- x^{2} + 8 x - 7}}{2 \sqrt{7 - x} \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7}} 
(9*sqrt(-7 - x^2 + 8*x) + sqrt(-1 + x)*sqrt(7 - x)*(-7 - x^2 + 8*x) - sqrt(-1 + x)*(-4 + x)^2*sqrt(7 - x))/(2*sqrt(-1 + x)*sqrt(7 - x)*sqrt(-7 - x^2 + 8*x))
Respuesta numérica [src] 
1.4142135623731*(-0.875 + x - 0.125*x^2)^0.5 + 1.70084012854152*(1 - 0.142857142857143*x)^(-0.5)*(-1.0 + x)^(-0.5) + 0.176776695296637*(-0.875 + x - 0.125*x^2)^(-0.5)*(4.0 - x)*(-4.0 + x)
1.4142135623731*(-0.875 + x - 0.125*x^2)^0.5 + 1.70084012854152*(1 - 0.142857142857143*x)^(-0.5)*(-1.0 + x)^(-0.5) + 0.176776695296637*(-0.875 + x - 0.125*x^2)^(-0.5)*(4.0 - x)*(-4.0 + x)
Potencias [src] 
   _______________                                                  
  /       2                                             ___         
\/  -7 - x  + 8*x      (-4 + x)*(4 - x)             3*\/ 6          
------------------ + -------------------- + ------------------------
        2                 _______________                    _______
                         /       2              ________    / 7   x 
                     2*\/  -7 - x  + 8*x    4*\/ -1 + x *  /  - - - 
                                                         \/   6   6
(4−x)(x−4)2−x2+8x−7+−x2+8x−72+36476−x6x−1\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\frac{7}{6} - \frac{x}{6}} \sqrt{x - 1}} 
   _______________                                                  
  /       2                       2                     ___         
\/  -7 - x  + 8*x          (4 - x)                  3*\/ 6          
------------------ - -------------------- + ------------------------
        2                 _______________                    _______
                         /       2              ________    / 7   x 
                     2*\/  -7 - x  + 8*x    4*\/ -1 + x *  /  - - - 
                                                         \/   6   6
−(4−x)22−x2+8x−7+−x2+8x−72+36476−x6x−1- \frac{\left(4 - x\right)^{2}}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\frac{7}{6} - \frac{x}{6}} \sqrt{x - 1}} 
   _______________                                                  
  /       2                       2                     ___         
\/  -7 - x  + 8*x          (4 - x)                  3*\/ 6          
------------------ - -------------------- + ------------------------
        2                 _______________         __________________
                         /       2               /          /7   x\ 
                     2*\/  -7 - x  + 8*x    4*  /  (-1 + x)*|- - -| 
                                              \/            \6   6/
−(4−x)22−x2+8x−7+−x2+8x−72+364(76−x6)(x−1)- \frac{\left(4 - x\right)^{2}}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\left(\frac{7}{6} - \frac{x}{6}\right) \left(x - 1\right)}} 
   _______________                                                  
  /       2                      ___                                
\/  -7 - x  + 8*x            3*\/ 6               (-4 + x)*(4 - x)  
------------------ + ------------------------ + --------------------
        2                  __________________        _______________
                          /          /7   x\        /       2       
                     4*  /  (-1 + x)*|- - -|    2*\/  -7 - x  + 8*x 
                       \/            \6   6/
(4−x)(x−4)2−x2+8x−7+−x2+8x−72+364(76−x6)(x−1)\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\left(\frac{7}{6} - \frac{x}{6}\right) \left(x - 1\right)}} 
sqrt(-7 - x^2 + 8*x)/2 + 3*sqrt(6)/(4*sqrt((-1 + x)*(7/6 - x/6))) + (-4 + x)*(4 - x)/(2*sqrt(-7 - x^2 + 8*x))
Combinatoria [src] 
 /       _______________                                                                                  \ 
 |      /       2               ________   _______          ________   _______      2   ________   _______| 
-\- 9*\/  -7 - x  + 8*x  + 23*\/ -1 + x *\/ 7 - x  - 16*x*\/ -1 + x *\/ 7 - x  + 2*x *\/ -1 + x *\/ 7 - x / 
------------------------------------------------------------------------------------------------------------
                                   ____________________   ________   _______                                
                               2*\/ -(-1 + x)*(-7 + x) *\/ -1 + x *\/ 7 - x
−2x27−xx−1−16x7−xx−1+237−xx−1−9−x2+8x−72−(x−7)(x−1)7−xx−1- \frac{2 x^{2} \sqrt{7 - x} \sqrt{x - 1} - 16 x \sqrt{7 - x} \sqrt{x - 1} + 23 \sqrt{7 - x} \sqrt{x - 1} - 9 \sqrt{- x^{2} + 8 x - 7}}{2 \sqrt{- \left(x - 7\right) \left(x - 1\right)} \sqrt{7 - x} \sqrt{x - 1}} 
-(-9*sqrt(-7 - x^2 + 8*x) + 23*sqrt(-1 + x)*sqrt(7 - x) - 16*x*sqrt(-1 + x)*sqrt(7 - x) + 2*x^2*sqrt(-1 + x)*sqrt(7 - x))/(2*sqrt(-(-1 + x)*(-7 + x))*sqrt(-1 + x)*sqrt(7 - x))
Denominador común [src] 
 /       _______________                                                                                  \ 
 |      /       2               ________   _______          ________   _______      2   ________   _______| 
-\- 9*\/  -7 - x  + 8*x  + 23*\/ -1 + x *\/ 7 - x  - 16*x*\/ -1 + x *\/ 7 - x  + 2*x *\/ -1 + x *\/ 7 - x / 
------------------------------------------------------------------------------------------------------------
                                                           _______________                                  
                                     ________   _______   /       2                                         
                                 2*\/ -1 + x *\/ 7 - x *\/  -7 - x  + 8*x
−2x27−xx−1−16x7−xx−1+237−xx−1−9−x2+8x−727−xx−1−x2+8x−7- \frac{2 x^{2} \sqrt{7 - x} \sqrt{x - 1} - 16 x \sqrt{7 - x} \sqrt{x - 1} + 23 \sqrt{7 - x} \sqrt{x - 1} - 9 \sqrt{- x^{2} + 8 x - 7}}{2 \sqrt{7 - x} \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7}} 
-(-9*sqrt(-7 - x^2 + 8*x) + 23*sqrt(-1 + x)*sqrt(7 - x) - 16*x*sqrt(-1 + x)*sqrt(7 - x) + 2*x^2*sqrt(-1 + x)*sqrt(7 - x))/(2*sqrt(-1 + x)*sqrt(7 - x)*sqrt(-7 - x^2 + 8*x))
Denominador racional [src] 
                     _______________                                                  _______________                                                  _______________                                                   _______________
         ________   /       2                ___   __________         2   ________   /       2               ___  2   __________       3   ________   /       2                  ___   __________            ________   /       2       
- 7728*\/ -1 + x *\/  -7 - x  + 8*x  - 504*\/ 6 *\/ 42 - 6*x  - 1440*x *\/ -1 + x *\/  -7 - x  + 8*x  - 72*\/ 6 *x *\/ 42 - 6*x  + 96*x *\/ -1 + x *\/  -7 - x  + 8*x  + 576*x*\/ 6 *\/ 42 - 6*x  + 6480*x*\/ -1 + x *\/  -7 - x  + 8*x 
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                                                                                                     ________             /     2      \                                                                                                
                                                                                                16*\/ -1 + x *(-42 + 6*x)*\7 + x  - 8*x/
96x3x−1−x2+8x−7−726x242−6x−1440x2x−1−x2+8x−7+5766x42−6x+6480xx−1−x2+8x−7−504642−6x−7728x−1−x2+8x−716x−1(6x−42)(x2−8x+7)\frac{96 x^{3} \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7} - 72 \sqrt{6} x^{2} \sqrt{42 - 6 x} - 1440 x^{2} \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7} + 576 \sqrt{6} x \sqrt{42 - 6 x} + 6480 x \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7} - 504 \sqrt{6} \sqrt{42 - 6 x} - 7728 \sqrt{x - 1} \sqrt{- x^{2} + 8 x - 7}}{16 \sqrt{x - 1} \left(6 x - 42\right) \left(x^{2} - 8 x + 7\right)} 
(-7728*sqrt(-1 + x)*sqrt(-7 - x^2 + 8*x) - 504*sqrt(6)*sqrt(42 - 6*x) - 1440*x^2*sqrt(-1 + x)*sqrt(-7 - x^2 + 8*x) - 72*sqrt(6)*x^2*sqrt(42 - 6*x) + 96*x^3*sqrt(-1 + x)*sqrt(-7 - x^2 + 8*x) + 576*x*sqrt(6)*sqrt(42 - 6*x) + 6480*x*sqrt(-1 + x)*sqrt(-7 - x^2 + 8*x))/(16*sqrt(-1 + x)*(-42 + 6*x)*(7 + x^2 - 8*x))
Compilar la expresión [src] 
   _______________                                                  
  /       2                                             ___         
\/  -7 - x  + 8*x      (-4 + x)*(4 - x)             3*\/ 6          
------------------ + -------------------- + ------------------------
        2                 _______________                    _______
                         /       2              ________    / 7   x 
                     2*\/  -7 - x  + 8*x    4*\/ -1 + x *  /  - - - 
                                                         \/   6   6
(4−x)(x−4)2−x2+8x−7+−x2+8x−72+36476−x6x−1\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\frac{7}{6} - \frac{x}{6}} \sqrt{x - 1}} 
sqrt(-7 - x^2 + 8*x)/2 + (-4 + x)*(4 - x)/(2*sqrt(-7 - x^2 + 8*x)) + 3*sqrt(6)/(4*sqrt(-1 + x)*sqrt(7/6 - x/6))
Abrimos la expresión [src] 
  _______________                                     ___        
\/ 8*x - x*x - 7      (4 - x)*(x - 4)             3*\/ 6         
----------------- + ------------------- + -----------------------
        2               _______________         _______          
                    2*\/ 8*x - x*x - 7         / 7   x    _______
                                          4*  /  - - - *\/ x - 1 
                                            \/   6   6
(4−x)(x−4)2(−xx+8x)−7+(−xx+8x)−72+364x−1−x6+76\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{\left(- x x + 8 x\right) - 7}} + \frac{\sqrt{\left(- x x + 8 x\right) - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{x - 1} \sqrt{- \frac{x}{6} + \frac{7}{6}}} 
sqrt(8*x - x*x - 7)/2 + (4 - x)*(x - 4)/(2*sqrt(8*x - x*x - 7)) + 3*sqrt(6)/(4*sqrt(7/6 - x/6)*sqrt(x - 1))
Parte trigonométrica [src] 
   _______________                                                  
  /       2                                             ___         
\/  -7 - x  + 8*x      (-4 + x)*(4 - x)             3*\/ 6          
------------------ + -------------------- + ------------------------
        2                 _______________                    _______
                         /       2              ________    / 7   x 
                     2*\/  -7 - x  + 8*x    4*\/ -1 + x *  /  - - - 
                                                         \/   6   6
(4−x)(x−4)2−x2+8x−7+−x2+8x−72+36476−x6x−1\frac{\left(4 - x\right) \left(x - 4\right)}{2 \sqrt{- x^{2} + 8 x - 7}} + \frac{\sqrt{- x^{2} + 8 x - 7}}{2} + \frac{3 \sqrt{6}}{4 \sqrt{\frac{7}{6} - \frac{x}{6}} \sqrt{x - 1}} 
sqrt(-7 - x^2 + 8*x)/2 + (-4 + x)*(4 - x)/(2*sqrt(-7 - x^2 + 8*x)) + 3*sqrt(6)/(4*sqrt(-1 + x)*sqrt(7/6 - x/6))
Unión de expresiones racionales [src] 
    ________________     ________   _______                                    
9*\/ -7 + x*(8 - x)  + \/ -1 + x *\/ 7 - x *(-7 + x*(8 - x) + (-4 + x)*(4 - x))
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                       ________   ________________   _______                   
                   2*\/ -1 + x *\/ -7 + x*(8 - x) *\/ 7 - x
7−xx−1(x(8−x)+(4−x)(x−4)−7)+9x(8−x)−727−xx−1x(8−x)−7\frac{\sqrt{7 - x} \sqrt{x - 1} \left(x \left(8 - x\right) + \left(4 - x\right) \left(x - 4\right) - 7\right) + 9 \sqrt{x \left(8 - x\right) - 7}}{2 \sqrt{7 - x} \sqrt{x - 1} \sqrt{x \left(8 - x\right) - 7}} 
(9*sqrt(-7 + x*(8 - x)) + sqrt(-1 + x)*sqrt(7 - x)*(-7 + x*(8 - x) + (-4 + x)*(4 - x)))/(2*sqrt(-1 + x)*sqrt(-7 + x*(8 - x))*sqrt(7 - x))
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