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¿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)))))))-(y/(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*|y + ------------------| - ------------
  |            _________ |      _________
  |           /  2    2  |     /  2    2 
  \     x + \/  x  + y   /   \/  x  + y  
$$y \left(y + \frac{\frac{2 x}{2 \sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y*(y + (1 + (2*x)/((2*sqrt(x^2 + y^2))))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)
Descomposición de una fracción [src]
y^2
$$y^{2}$$
 2
y 
Simplificación general [src]
 2
y 
$$y^{2}$$
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*(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)) - y*(x^2 + y^2)^(-0.5)
Denominador común [src]
 2
y 
$$y^{2}$$
y^2
Unión de expresiones racionales [src]
 2
y 
$$y^{2}$$
y^2
Abrimos la expresión [src]
  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y  
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)
Compilar la expresión [src]
  /                            x      \
  |                   1 + ------------|
  |                          _________|
  |                         /  2    2 |
  |         1             \/  x  + y  |
y*|y - ------------ + ----------------|
  |       _________          _________|
  |      /  2    2          /  2    2 |
  \    \/  x  + y     x + \/  x  + y  /
$$y \left(y - \frac{1}{\sqrt{x^{2} + y^{2}}} + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$
  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y  
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)
Denominador racional [src]
                                    2
     2  4      4  2      2 / 2    2\ 
- 2*x *y  - 2*x *y  + 2*y *\x  + y / 
-------------------------------------
               2 / 2    2\           
            2*y *\x  + y /           
$$\frac{- 2 x^{4} y^{2} - 2 x^{2} y^{4} + 2 y^{2} \left(x^{2} + y^{2}\right)^{2}}{2 y^{2} \left(x^{2} + y^{2}\right)}$$
(-2*x^2*y^4 - 2*x^4*y^2 + 2*y^2*(x^2 + y^2)^2)/(2*y^2*(x^2 + y^2))
Combinatoria [src]
 2
y 
$$y^{2}$$
y^2
Potencias [src]
  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y  
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)
Parte trigonométrica [src]
  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y  
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)