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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(7)*(sqrt(7)+7*x)/(7*sqrt(7*x^2-4)*(sqrt(7)*x+sqrt(7*x^2-4)))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
             ___ /  ___      \           
           \/ 7 *\\/ 7  + 7*x/           
-----------------------------------------
     __________ /             __________\
    /    2      |  ___       /    2     |
7*\/  7*x  - 4 *\\/ 7 *x + \/  7*x  - 4 /
7(7x+7)77x2−4(7x+7x2−4)\frac{\sqrt{7} \left(7 x + \sqrt{7}\right)}{7 \sqrt{7 x^{2} - 4} \left(\sqrt{7} x + \sqrt{7 x^{2} - 4}\right)} 
(sqrt(7)*(sqrt(7) + 7*x))/(((7*sqrt(7*x^2 - 4))*(sqrt(7)*x + sqrt(7*x^2 - 4))))
Simplificación general [src] 
                   ___            
           1 + x*\/ 7             
----------------------------------
                       ___________
        2       ___   /         2 
-4 + 7*x  + x*\/ 7 *\/  -4 + 7*x
7x+17x2+7x7x2−4−4\frac{\sqrt{7} x + 1}{7 x^{2} + \sqrt{7} x \sqrt{7 x^{2} - 4} - 4} 
(1 + x*sqrt(7))/(-4 + 7*x^2 + x*sqrt(7)*sqrt(-4 + 7*x^2))
Respuesta numérica [src] 
0.0539949247156039*(-0.571428571428571 + x^2)^(-0.5)*(7.0 + 18.5202591774521*x)/(2.64575131106459*x + 2.64575131106459*(-0.571428571428571 + x^2)^0.5)
0.0539949247156039*(-0.571428571428571 + x^2)^(-0.5)*(7.0 + 18.5202591774521*x)/(2.64575131106459*x + 2.64575131106459*(-0.571428571428571 + x^2)^0.5)
Denominador común [src] 
                   ___            
           1 + x*\/ 7             
----------------------------------
                       ___________
        2       ___   /         2 
-4 + 7*x  + x*\/ 7 *\/  -4 + 7*x
7x+17x2+7x7x2−4−4\frac{\sqrt{7} x + 1}{7 x^{2} + \sqrt{7} x \sqrt{7 x^{2} - 4} - 4} 
(1 + x*sqrt(7))/(-4 + 7*x^2 + x*sqrt(7)*sqrt(-4 + 7*x^2))
Potencias [src] 
               ___ /  ___      \             
             \/ 7 *\\/ 7  + 7*x/             
---------------------------------------------
   ___________ /     ___________            \
  /         2  |    /         2          ___|
\/  -4 + 7*x  *\7*\/  -4 + 7*x   + 7*x*\/ 7 /
7(7x+7)7x2−4(77x+77x2−4)\frac{\sqrt{7} \left(7 x + \sqrt{7}\right)}{\sqrt{7 x^{2} - 4} \left(7 \sqrt{7} x + 7 \sqrt{7 x^{2} - 4}\right)} 
sqrt(7)*(sqrt(7) + 7*x)/(sqrt(-4 + 7*x^2)*(7*sqrt(-4 + 7*x^2) + 7*x*sqrt(7)))
Denominador racional [src] 
                                            ___________              ___________
       2       ___  3         ___      2   /         2        ___   /         2 
4 - 7*x  - 7*\/ 7 *x  + 4*x*\/ 7  + 7*x *\/  -4 + 7*x   + x*\/ 7 *\/  -4 + 7*x  
--------------------------------------------------------------------------------
                                            2                                   
                                  -16 + 28*x
−77x3+7x27x2−4−7x2+7x7x2−4+47x+428x2−16\frac{- 7 \sqrt{7} x^{3} + 7 x^{2} \sqrt{7 x^{2} - 4} - 7 x^{2} + \sqrt{7} x \sqrt{7 x^{2} - 4} + 4 \sqrt{7} x + 4}{28 x^{2} - 16} 
(4 - 7*x^2 - 7*sqrt(7)*x^3 + 4*x*sqrt(7) + 7*x^2*sqrt(-4 + 7*x^2) + x*sqrt(7)*sqrt(-4 + 7*x^2))/(-16 + 28*x^2)
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