Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x^2-2*x)*(1/(sqrt(x^2-2*x))-(-1+x)*(x+1)/(x^2-2*x)^(3/2))/(3*(x+1))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   __________                                   
  /  2        /      1         (-1 + x)*(x + 1)\
\/  x  - 2*x *|------------- - ----------------|
              |   __________              3/2  |
              |  /  2           / 2      \     |
              \\/  x  - 2*x     \x  - 2*x/     /
------------------------------------------------
                   3*(x + 1)
x2−2x(−(x−1)(x+1)(x2−2x)32+1x2−2x)3(x+1)\frac{\sqrt{x^{2} - 2 x} \left(- \frac{\left(x - 1\right) \left(x + 1\right)}{\left(x^{2} - 2 x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 2 x}}\right)}{3 \left(x + 1\right)} 
(sqrt(x^2 - 2*x)*(1/(sqrt(x^2 - 2*x)) - (-1 + x)*(x + 1)/(x^2 - 2*x)^(3/2)))/((3*(x + 1)))
Descomposición de una fracción [src] 
-1/(6*x) - 1/(6*(-2 + x)) + 1/(3*(1 + x))
13(x+1)−16(x−2)−16x\frac{1}{3 \left(x + 1\right)} - \frac{1}{6 \left(x - 2\right)} - \frac{1}{6 x} 
   1        1            1    
- --- - ---------- + ---------
  6*x   6*(-2 + x)   3*(1 + x)
Simplificación general [src] 
    -1 + 2*x    
----------------
    /         2\
3*x*\2 + x - x /
2x−13x(−x2+x+2)\frac{2 x - 1}{3 x \left(- x^{2} + x + 2\right)} 
(-1 + 2*x)/(3*x*(2 + x - x^2))
Respuesta numérica [src] 
1.4142135623731*(-x + 0.5*x^2)^0.5*(0.707106781186547*(-x + 0.5*x^2)^(-0.5) - 0.353553390593274*(-x + 0.5*x^2)^(-1.5)*(1.0 + x)*(-1.0 + x))/(3.0 + 3.0*x)
1.4142135623731*(-x + 0.5*x^2)^0.5*(0.707106781186547*(-x + 0.5*x^2)^(-0.5) - 0.353553390593274*(-x + 0.5*x^2)^(-1.5)*(1.0 + x)*(-1.0 + x))/(3.0 + 3.0*x)
Combinatoria [src] 
    -(-1 + 2*x)     
--------------------
3*x*(1 + x)*(-2 + x)
−2x−13x(x−2)(x+1)- \frac{2 x - 1}{3 x \left(x - 2\right) \left(x + 1\right)} 
-(-1 + 2*x)/(3*x*(1 + x)*(-2 + x))
Denominador común [src] 
   -(-1 + 2*x)    
------------------
          2      3
-6*x - 3*x  + 3*x
−2x−13x3−3x2−6x- \frac{2 x - 1}{3 x^{3} - 3 x^{2} - 6 x} 
-(-1 + 2*x)/(-6*x - 3*x^2 + 3*x^3)
Unión de expresiones racionales [src] 
x*(-2 + x) - (1 + x)*(-1 + x)
-----------------------------
     x*(-2 + x)*(3 + 3*x)
x(x−2)−(x−1)(x+1)x(x−2)(3x+3)\frac{x \left(x - 2\right) - \left(x - 1\right) \left(x + 1\right)}{x \left(x - 2\right) \left(3 x + 3\right)} 
(x*(-2 + x) - (1 + x)*(-1 + x))/(x*(-2 + x)*(3 + 3*x))
Parte trigonométrica [src] 
   __________                                   
  /  2        /      1         (1 + x)*(-1 + x)\
\/  x  - 2*x *|------------- - ----------------|
              |   __________              3/2  |
              |  /  2           / 2      \     |
              \\/  x  - 2*x     \x  - 2*x/     /
------------------------------------------------
                    3 + 3*x
x2−2x(−(x−1)(x+1)(x2−2x)32+1x2−2x)3x+3\frac{\sqrt{x^{2} - 2 x} \left(- \frac{\left(x - 1\right) \left(x + 1\right)}{\left(x^{2} - 2 x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 2 x}}\right)}{3 x + 3} 
sqrt(x^2 - 2*x)*(1/sqrt(x^2 - 2*x) - (1 + x)*(-1 + x)/(x^2 - 2*x)^(3/2))/(3 + 3*x)
Compilar la expresión [src] 
   __________                                   
  /  2        /      1         (1 + x)*(-1 + x)\
\/  x  - 2*x *|------------- - ----------------|
              |   __________              3/2  |
              |  /  2           / 2      \     |
              \\/  x  - 2*x     \x  - 2*x/     /
------------------------------------------------
                    3 + 3*x
x2−2x(−(x−1)(x+1)(x2−2x)32+1x2−2x)3x+3\frac{\sqrt{x^{2} - 2 x} \left(- \frac{\left(x - 1\right) \left(x + 1\right)}{\left(x^{2} - 2 x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 2 x}}\right)}{3 x + 3} 
sqrt(x^2 - 2*x)*(1/sqrt(x^2 - 2*x) - (1 + x)*(-1 + x)/(x^2 - 2*x)^(3/2))/(3 + 3*x)
Denominador racional [src] 
               2                  
 2   / 2      \     4            3
x  + \x  - 2*x/  - x  - 2*x + 2*x 
----------------------------------
             / 4      3      2\   
   (3 + 3*x)*\x  - 4*x  + 4*x /
−x4+2x3+x2−2x+(x2−2x)2(3x+3)(x4−4x3+4x2)\frac{- x^{4} + 2 x^{3} + x^{2} - 2 x + \left(x^{2} - 2 x\right)^{2}}{\left(3 x + 3\right) \left(x^{4} - 4 x^{3} + 4 x^{2}\right)} 
(x^2 + (x^2 - 2*x)^2 - x^4 - 2*x + 2*x^3)/((3 + 3*x)*(x^4 - 4*x^3 + 4*x^2))
Potencias [src] 
   __________                                   
  /  2        /      1         (1 + x)*(-1 + x)\
\/  x  - 2*x *|------------- - ----------------|
              |   __________              3/2  |
              |  /  2           / 2      \     |
              \\/  x  - 2*x     \x  - 2*x/     /
------------------------------------------------
                    3 + 3*x
x2−2x(−(x−1)(x+1)(x2−2x)32+1x2−2x)3x+3\frac{\sqrt{x^{2} - 2 x} \left(- \frac{\left(x - 1\right) \left(x + 1\right)}{\left(x^{2} - 2 x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 2 x}}\right)}{3 x + 3} 
sqrt(x^2 - 2*x)*(1/sqrt(x^2 - 2*x) - (1 + x)*(-1 + x)/(x^2 - 2*x)^(3/2))/(3 + 3*x)
    © Sr Examen – Калькулятор