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Simplificación de expresiones/ Descomposición en fracciones simples/ y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))

¿Cómo vas a descomponer esta y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2))))))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  /             2*x      \
  |    1 + --------------|
  |             _________|
  |            /  2    2 |
  |        2*\/  x  + y  |
y*|y + ------------------|
  |            _________ |
  |           /  2    2  |
  \     x + \/  x  + y   /
y(y+2x2x2+y2+1x+x2+y2)y \left(y + \frac{\frac{2 x}{2 \sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) 
y*(y + (1 + (2*x)/((2*sqrt(x^2 + y^2))))/(x + sqrt(x^2 + y^2)))
Simplificación general [src] 
 2        y      
y  + ------------
        _________
       /  2    2 
     \/  x  + y
y2+yx2+y2y^{2} + \frac{y}{\sqrt{x^{2} + y^{2}}} 
y^2 + y/sqrt(x^2 + y^2)
Respuesta numérica [src] 
y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5))
y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5))
Abrimos la expresión [src] 
  /             x      \
  |    1 + ------------|
  |           _________|
  |          /  2    2 |
  |        \/  x  + y  |
y*|y + ----------------|
  |           _________|
  |          /  2    2 |
  \    x + \/  x  + y  /
y(y+xx2+y2+1x+x2+y2)y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) 
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
Denominador racional [src] 
                    3/2             _________
   2       / 2    2\           2   /  2    2 
2*y  + 2*y*\x  + y /    - 2*y*x *\/  x  + y  
---------------------------------------------
                      _________              
                     /  2    2               
               2*y*\/  x  + y
−2x2yx2+y2+2y2+2y(x2+y2)322yx2+y2\frac{- 2 x^{2} y \sqrt{x^{2} + y^{2}} + 2 y^{2} + 2 y \left(x^{2} + y^{2}\right)^{\frac{3}{2}}}{2 y \sqrt{x^{2} + y^{2}}} 
(2*y^2 + 2*y*(x^2 + y^2)^(3/2) - 2*y*x^2*sqrt(x^2 + y^2))/(2*y*sqrt(x^2 + y^2))
Compilar la expresión [src] 
  /             x      \
  |    1 + ------------|
  |           _________|
  |          /  2    2 |
  |        \/  x  + y  |
y*|y + ----------------|
  |           _________|
  |          /  2    2 |
  \    x + \/  x  + y  /
y(y+xx2+y2+1x+x2+y2)y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) 
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
Combinatoria [src] 
  /         _________\
  |        /  2    2 |
y*\1 + y*\/  x  + y  /
----------------------
        _________     
       /  2    2      
     \/  x  + y
y(yx2+y2+1)x2+y2\frac{y \left(y \sqrt{x^{2} + y^{2}} + 1\right)}{\sqrt{x^{2} + y^{2}}} 
y*(1 + y*sqrt(x^2 + y^2))/sqrt(x^2 + y^2)
Parte trigonométrica [src] 
  /             x      \
  |    1 + ------------|
  |           _________|
  |          /  2    2 |
  |        \/  x  + y  |
y*|y + ----------------|
  |           _________|
  |          /  2    2 |
  \    x + \/  x  + y  /
y(y+xx2+y2+1x+x2+y2)y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) 
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
Unión de expresiones racionales [src] 
  /         _________\
  |        /  2    2 |
y*\1 + y*\/  x  + y  /
----------------------
        _________     
       /  2    2      
     \/  x  + y
y(yx2+y2+1)x2+y2\frac{y \left(y \sqrt{x^{2} + y^{2}} + 1\right)}{\sqrt{x^{2} + y^{2}}} 
y*(1 + y*sqrt(x^2 + y^2))/sqrt(x^2 + y^2)
Denominador común [src] 
                  _________  
                 /  2    2   
 2     x*y + y*\/  x  + y    
y  + ------------------------
                    _________
      2    2       /  2    2 
     x  + y  + x*\/  x  + y
y2+xy+yx2+y2x2+xx2+y2+y2y^{2} + \frac{x y + y \sqrt{x^{2} + y^{2}}}{x^{2} + x \sqrt{x^{2} + y^{2}} + y^{2}} 
y^2 + (x*y + y*sqrt(x^2 + y^2))/(x^2 + y^2 + x*sqrt(x^2 + y^2))
Potencias [src] 
  /             x      \
  |    1 + ------------|
  |           _________|
  |          /  2    2 |
  |        \/  x  + y  |
y*|y + ----------------|
  |           _________|
  |          /  2    2 |
  \    x + \/  x  + y  /
y(y+xx2+y2+1x+x2+y2)y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) 
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
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