Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x^2-4*x+9)*(-5-2*x)/(x^2+5*x+1)^2+(-2+x)/(sqrt(x^2-4*x+9)*(x^2+5*x+1))

¿Cómo vas a descomponer esta sqrt(x^2-4*x+9)*(-5-2*x)/(x^2+5*x+1)^2+(-2+x)/(sqrt(x^2-4*x+9)*(x^2+5*x+1)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   ______________                                              
  /  2                                                         
\/  x  - 4*x + 9 *(-5 - 2*x)                -2 + x             
---------------------------- + --------------------------------
                    2             ______________               
      / 2          \             /  2            / 2          \
      \x  + 5*x + 1/           \/  x  - 4*x + 9 *\x  + 5*x + 1/
(−2x−5)(x2−4x)+9((x2+5x)+1)2+x−2(x2−4x)+9((x2+5x)+1)\frac{\left(- 2 x - 5\right) \sqrt{\left(x^{2} - 4 x\right) + 9}}{\left(\left(x^{2} + 5 x\right) + 1\right)^{2}} + \frac{x - 2}{\sqrt{\left(x^{2} - 4 x\right) + 9} \left(\left(x^{2} + 5 x\right) + 1\right)} 
(sqrt(x^2 - 4*x + 9)*(-5 - 2*x))/(x^2 + 5*x + 1)^2 + (-2 + x)/((sqrt(x^2 - 4*x + 9)*(x^2 + 5*x + 1)))
Simplificación general [src] 
                     3            2              
              -47 - x  - 7*x + 6*x               
-------------------------------------------------
   ______________                                
  /      2        /     4              3       2\
\/  9 + x  - 4*x *\1 + x  + 10*x + 10*x  + 27*x /
−x3+6x2−7x−47x2−4x+9(x4+10x3+27x2+10x+1)\frac{- x^{3} + 6 x^{2} - 7 x - 47}{\sqrt{x^{2} - 4 x + 9} \left(x^{4} + 10 x^{3} + 27 x^{2} + 10 x + 1\right)} 
(-47 - x^3 - 7*x + 6*x^2)/(sqrt(9 + x^2 - 4*x)*(1 + x^4 + 10*x + 10*x^3 + 27*x^2))
Respuesta numérica [src] 
0.12*(1 + 0.111111111111111*x^2 - 0.444444444444444*x)^0.5*(-5.0 - 2.0*x)/(0.2 + x + 0.2*x^2)^2 + 0.333333333333333*(1 + 0.111111111111111*x^2 - 0.444444444444444*x)^(-0.5)*(-2.0 + x)/(1.0 + x^2 + 5.0*x)
0.12*(1 + 0.111111111111111*x^2 - 0.444444444444444*x)^0.5*(-5.0 - 2.0*x)/(0.2 + x + 0.2*x^2)^2 + 0.333333333333333*(1 + 0.111111111111111*x^2 - 0.444444444444444*x)^(-0.5)*(-2.0 + x)/(1.0 + x^2 + 5.0*x)
Parte trigonométrica [src] 
                                      ______________           
                                     /      2                  
             -2 + x                \/  9 + x  - 4*x *(-5 - 2*x)
-------------------------------- + ----------------------------
                  ______________                       2       
/     2      \   /      2                /     2      \        
\1 + x  + 5*x/*\/  9 + x  - 4*x          \1 + x  + 5*x/
(−2x−5)x2−4x+9(x2+5x+1)2+x−2x2−4x+9(x2+5x+1)\frac{\left(- 2 x - 5\right) \sqrt{x^{2} - 4 x + 9}}{\left(x^{2} + 5 x + 1\right)^{2}} + \frac{x - 2}{\sqrt{x^{2} - 4 x + 9} \left(x^{2} + 5 x + 1\right)} 
(-2 + x)/((1 + x^2 + 5*x)*sqrt(9 + x^2 - 4*x)) + sqrt(9 + x^2 - 4*x)*(-5 - 2*x)/(1 + x^2 + 5*x)^2
Unión de expresiones racionales [src] 
(1 + x*(5 + x))*(-2 + x) + (-5 - 2*x)*(9 + x*(-4 + x))
------------------------------------------------------
                        2   ________________          
         (1 + x*(5 + x)) *\/ 9 + x*(-4 + x)
(−2x−5)(x(x−4)+9)+(x−2)(x(x+5)+1)x(x−4)+9(x(x+5)+1)2\frac{\left(- 2 x - 5\right) \left(x \left(x - 4\right) + 9\right) + \left(x - 2\right) \left(x \left(x + 5\right) + 1\right)}{\sqrt{x \left(x - 4\right) + 9} \left(x \left(x + 5\right) + 1\right)^{2}} 
((1 + x*(5 + x))*(-2 + x) + (-5 - 2*x)*(9 + x*(-4 + x)))/((1 + x*(5 + x))^2*sqrt(9 + x*(-4 + x)))
Potencias [src] 
                                      ______________           
                                     /      2                  
             -2 + x                \/  9 + x  - 4*x *(-5 - 2*x)
-------------------------------- + ----------------------------
                  ______________                       2       
/     2      \   /      2                /     2      \        
\1 + x  + 5*x/*\/  9 + x  - 4*x          \1 + x  + 5*x/
(−2x−5)x2−4x+9(x2+5x+1)2+x−2x2−4x+9(x2+5x+1)\frac{\left(- 2 x - 5\right) \sqrt{x^{2} - 4 x + 9}}{\left(x^{2} + 5 x + 1\right)^{2}} + \frac{x - 2}{\sqrt{x^{2} - 4 x + 9} \left(x^{2} + 5 x + 1\right)} 
(-2 + x)/((1 + x^2 + 5*x)*sqrt(9 + x^2 - 4*x)) + sqrt(9 + x^2 - 4*x)*(-5 - 2*x)/(1 + x^2 + 5*x)^2
Combinatoria [src] 
      /      3      2      \     
     -\47 + x  - 6*x  + 7*x/     
---------------------------------
              2    ______________
/     2      \    /      2       
\1 + x  + 5*x/ *\/  9 + x  - 4*x
−x3−6x2+7x+47x2−4x+9(x2+5x+1)2- \frac{x^{3} - 6 x^{2} + 7 x + 47}{\sqrt{x^{2} - 4 x + 9} \left(x^{2} + 5 x + 1\right)^{2}} 
-(47 + x^3 - 6*x^2 + 7*x)/((1 + x^2 + 5*x)^2*sqrt(9 + x^2 - 4*x))
Compilar la expresión [src] 
                                      ______________           
                                     /      2                  
             -2 + x                \/  9 + x  - 4*x *(-5 - 2*x)
-------------------------------- + ----------------------------
                  ______________                       2       
/     2      \   /      2                /     2      \        
\1 + x  + 5*x/*\/  9 + x  - 4*x          \1 + x  + 5*x/
(−2x−5)x2−4x+9(x2+5x+1)2+x−2x2−4x+9(x2+5x+1)\frac{\left(- 2 x - 5\right) \sqrt{x^{2} - 4 x + 9}}{\left(x^{2} + 5 x + 1\right)^{2}} + \frac{x - 2}{\sqrt{x^{2} - 4 x + 9} \left(x^{2} + 5 x + 1\right)} 
(-2 + x)/((1 + x^2 + 5*x)*sqrt(9 + x^2 - 4*x)) + sqrt(9 + x^2 - 4*x)*(-5 - 2*x)/(1 + x^2 + 5*x)^2
Denominador racional [src] 
                                                    2                           2
                  2      4      5     /     2      \        3     /     2      \ 
-45 - 223*x - 32*x  - 7*x  - 2*x  - 2*\1 + x  + 5*x/  + 15*x  + x*\1 + x  + 5*x/ 
---------------------------------------------------------------------------------
                                      3    ______________                        
                        /     2      \    /      2                               
                        \1 + x  + 5*x/ *\/  9 + x  - 4*x
−2x5−7x4+15x3−32x2+x(x2+5x+1)2−223x−2(x2+5x+1)2−45x2−4x+9(x2+5x+1)3\frac{- 2 x^{5} - 7 x^{4} + 15 x^{3} - 32 x^{2} + x \left(x^{2} + 5 x + 1\right)^{2} - 223 x - 2 \left(x^{2} + 5 x + 1\right)^{2} - 45}{\sqrt{x^{2} - 4 x + 9} \left(x^{2} + 5 x + 1\right)^{3}} 
(-45 - 223*x - 32*x^2 - 7*x^4 - 2*x^5 - 2*(1 + x^2 + 5*x)^2 + 15*x^3 + x*(1 + x^2 + 5*x)^2)/((1 + x^2 + 5*x)^3*sqrt(9 + x^2 - 4*x))
Denominador común [src] 
                                                /      3      2      \                                               
                                               -\47 + x  - 6*x  + 7*x/                                               
---------------------------------------------------------------------------------------------------------------------
   ______________         ______________           ______________            ______________            ______________
  /      2           4   /      2                 /      2              3   /      2              2   /      2       
\/  9 + x  - 4*x  + x *\/  9 + x  - 4*x  + 10*x*\/  9 + x  - 4*x  + 10*x *\/  9 + x  - 4*x  + 27*x *\/  9 + x  - 4*x
−x3−6x2+7x+47x4x2−4x+9+10x3x2−4x+9+27x2x2−4x+9+10xx2−4x+9+x2−4x+9- \frac{x^{3} - 6 x^{2} + 7 x + 47}{x^{4} \sqrt{x^{2} - 4 x + 9} + 10 x^{3} \sqrt{x^{2} - 4 x + 9} + 27 x^{2} \sqrt{x^{2} - 4 x + 9} + 10 x \sqrt{x^{2} - 4 x + 9} + \sqrt{x^{2} - 4 x + 9}} 
-(47 + x^3 - 6*x^2 + 7*x)/(sqrt(9 + x^2 - 4*x) + x^4*sqrt(9 + x^2 - 4*x) + 10*x*sqrt(9 + x^2 - 4*x) + 10*x^3*sqrt(9 + x^2 - 4*x) + 27*x^2*sqrt(9 + x^2 - 4*x))
    © Sr Examen – Калькулятор