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

Expresión a simplificar:

Solución

Ha introducido [src]
                /                              2 \
  _____________ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x*(-2 + x) *|1 - ------ - ------ + ----------|
                \      x      -2 + x   x*(-2 + x)/
--------------------------------------------------
                    x*(-2 + x)                    
x(x2)(((1x1x)x1x2)+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(\left(\left(1 - \frac{x - 1}{x}\right) - \frac{x - 1}{x - 2}\right) + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
(sqrt((-x)*(-2 + x))*(1 - (-1 + x)/x - (-1 + x)/(-2 + x) + (-1 + x)^2/((x*(-2 + x)))))/((x*(-2 + x)))
Simplificación general [src]
   _____________ 
-\/ -x*(-2 + x)  
-----------------
 2 /     2      \
x *\4 + x  - 4*x/
x(x2)x2(x24x+4)- \frac{\sqrt{- x \left(x - 2\right)}}{x^{2} \left(x^{2} - 4 x + 4\right)}
-sqrt(-x*(-2 + x))/(x^2*(4 + x^2 - 4*x))
Respuesta numérica [src]
(-x*(-2.0 + x))^0.5*(1.0 - (-1.0 + x)/x - (-1.0 + x)/(-2.0 + x) + (-1.0 + x)^2/(x*(-2.0 + x)))/(x*(-2.0 + x))
(-x*(-2.0 + x))^0.5*(1.0 - (-1.0 + x)/x - (-1.0 + x)/(-2.0 + x) + (-1.0 + x)^2/(x*(-2.0 + x)))/(x*(-2.0 + x))
Denominador racional [src]
  _____________ /                 2            \
\/ -x*(-2 + x) *\-2 + x + (-1 + x)  + x*(1 - x)/
------------------------------------------------
                   2         2                  
                  x *(-2 + x)                   
x(x2)(x(1x)+x+(x1)22)x2(x2)2\frac{\sqrt{- x \left(x - 2\right)} \left(x \left(1 - x\right) + x + \left(x - 1\right)^{2} - 2\right)}{x^{2} \left(x - 2\right)^{2}}
sqrt(-x*(-2 + x))*(-2 + x + (-1 + x)^2 + x*(1 - x))/(x^2*(-2 + x)^2)
Compilar la expresión [src]
                /                              2 \
  _____________ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x*(-2 + x) *|1 - ------ - ------ + ----------|
                \      x      -2 + x   x*(-2 + x)/
--------------------------------------------------
                    x*(-2 + x)                    
x(x2)(1x1x2x1x+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(1 - \frac{x - 1}{x - 2} - \frac{x - 1}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
sqrt(-x*(-2 + x))*(1 - (-1 + x)/x - (-1 + x)/(-2 + x) + (-1 + x)^2/(x*(-2 + x)))/(x*(-2 + x))
Unión de expresiones racionales [src]
  _____________ /                 2             \
\/ -x*(-2 + x) *\-2 + x + (-1 + x)  - x*(-1 + x)/
-------------------------------------------------
                    2         2                  
                   x *(-2 + x)                   
x(x2)(x(x1)+x+(x1)22)x2(x2)2\frac{\sqrt{- x \left(x - 2\right)} \left(- x \left(x - 1\right) + x + \left(x - 1\right)^{2} - 2\right)}{x^{2} \left(x - 2\right)^{2}}
sqrt(-x*(-2 + x))*(-2 + x + (-1 + x)^2 - x*(-1 + x))/(x^2*(-2 + x)^2)
Abrimos la expresión [src]
       /                              2 \
  ____ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x *|1 - ------ - ------ + ----------|
       \      x      -2 + x   x*(-2 + x)/
-----------------------------------------
                   ________              
               x*\/ -2 + x               
x(1x1x2x1x+(x1)2x(x2))xx2\frac{\sqrt{- x} \left(1 - \frac{x - 1}{x - 2} - \frac{x - 1}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \sqrt{x - 2}}
                /                              2 \
  _____________ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x*(-2 + x) *|1 - ------ - ------ + ----------|
                \      x      -2 + x   x*(-2 + x)/
--------------------------------------------------
                    x*(-2 + x)                    
x(x2)(1x1x2x1x+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(1 - \frac{x - 1}{x - 2} - \frac{x - 1}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
sqrt(-x*(-2 + x))*(1 - (-1 + x)/x - (-1 + x)/(-2 + x) + (-1 + x)^2/(x*(-2 + x)))/(x*(-2 + x))
Denominador común [src]
    ____________ 
   /    2        
-\/  - x  + 2*x  
-----------------
  4      3      2
 x  - 4*x  + 4*x 
x2+2xx44x3+4x2- \frac{\sqrt{- x^{2} + 2 x}}{x^{4} - 4 x^{3} + 4 x^{2}}
-sqrt(-x^2 + 2*x)/(x^4 - 4*x^3 + 4*x^2)
Combinatoria [src]
   _____________ 
-\/ -x*(-2 + x)  
-----------------
    2         2  
   x *(-2 + x)   
x(x2)x2(x2)2- \frac{\sqrt{- x \left(x - 2\right)}}{x^{2} \left(x - 2\right)^{2}}
-sqrt(-x*(-2 + x))/(x^2*(-2 + x)^2)
Potencias [src]
                /                             2 \
  _____________ |    1 - x   1 - x    (-1 + x)  |
\/ -x*(-2 + x) *|1 + ----- + ------ + ----------|
                \      x     -2 + x   x*(-2 + x)/
-------------------------------------------------
                    x*(-2 + x)                   
x(x2)(1xx2+1+1xx+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(\frac{1 - x}{x - 2} + 1 + \frac{1 - x}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
                /                              2 \
  _____________ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x*(-2 + x) *|1 - ------ - ------ + ----------|
                \      x      -2 + x   x*(-2 + x)/
--------------------------------------------------
                    x*(-2 + x)                    
x(x2)(1x1x2x1x+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(1 - \frac{x - 1}{x - 2} - \frac{x - 1}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
sqrt(-x*(-2 + x))*(1 - (-1 + x)/x - (-1 + x)/(-2 + x) + (-1 + x)^2/(x*(-2 + x)))/(x*(-2 + x))
Parte trigonométrica [src]
                /                              2 \
  _____________ |    -1 + x   -1 + x   (-1 + x)  |
\/ -x*(-2 + x) *|1 - ------ - ------ + ----------|
                \      x      -2 + x   x*(-2 + x)/
--------------------------------------------------
                    x*(-2 + x)                    
x(x2)(1x1x2x1x+(x1)2x(x2))x(x2)\frac{\sqrt{- x \left(x - 2\right)} \left(1 - \frac{x - 1}{x - 2} - \frac{x - 1}{x} + \frac{\left(x - 1\right)^{2}}{x \left(x - 2\right)}\right)}{x \left(x - 2\right)}
sqrt(-x*(-2 + x))*(1 - (-1 + x)/x - (-1 + x)/(-2 + x) + (-1 + x)^2/(x*(-2 + x)))/(x*(-2 + x))