Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(a*a-(x-a)/2*(x-a)/2)/2+(a+x)*(-x/4+a/4)/(2*sqrt(a*a-(x-a)/2*(x-a)/2))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
      _____________________                                
     /       x - a                                         
    /        -----*(x - a)                                 
   /           2                            /-x    a\      
  /    a*a - -------------          (a + x)*|--- + -|      
\/                 2                        \ 4    4/      
--------------------------- + -----------------------------
             2                        _____________________
                                     /       x - a         
                                    /        -----*(x - a) 
                                   /           2           
                              2*  /    a*a - ------------- 
                                \/                 2
(a+x)(a4+(−1)x4)2aa−−a+x2(−a+x)2+aa−−a+x2(−a+x)22\frac{\left(a + x\right) \left(\frac{a}{4} + \frac{\left(-1\right) x}{4}\right)}{2 \sqrt{a a - \frac{\frac{- a + x}{2} \left(- a + x\right)}{2}}} + \frac{\sqrt{a a - \frac{\frac{- a + x}{2} \left(- a + x\right)}{2}}}{2} 
sqrt(a*a - ((x - a)/2)*(x - a)/2)/2 + ((a + x)*((-x)/4 + a/4))/((2*sqrt(a*a - ((x - a)/2)*(x - a)/2)))
Simplificación general [src] 
         2      2                  
- (a - x)  + 4*a  + (a + x)*(a - x)
-----------------------------------
           ___________________     
          /          2      2      
      4*\/  - (a - x)  + 4*a
4a2−(a−x)2+(a−x)(a+x)44a2−(a−x)2\frac{4 a^{2} - \left(a - x\right)^{2} + \left(a - x\right) \left(a + x\right)}{4 \sqrt{4 a^{2} - \left(a - x\right)^{2}}} 
(-(a - x)^2 + 4*a^2 + (a + x)*(a - x))/(4*sqrt(-(a - x)^2 + 4*a^2))
Denominador común [src] 
    / 2      2      \     
   -\x  - 2*a  - a*x/     
--------------------------
     _____________________
    /    2      2         
2*\/  - x  + 3*a  + 2*a*x
−−2a2−ax+x223a2+2ax−x2- \frac{- 2 a^{2} - a x + x^{2}}{2 \sqrt{3 a^{2} + 2 a x - x^{2}}} 
-(x^2 - 2*a^2 - a*x)/(2*sqrt(-x^2 + 3*a^2 + 2*a*x))
Parte trigonométrica [src] 
      ______________________                                 
     /              /x   a\                                  
    /       (x - a)*|- - -|                                  
   /    2           \2   2/                  /  x   a\       
  /    a  - ---------------          (a + x)*|- - + -|       
\/                 2                         \  4   4/       
---------------------------- + ------------------------------
             2                         ______________________
                                      /              /x   a\ 
                                     /       (x - a)*|- - -| 
                                    /    2           \2   2/ 
                               2*  /    a  - --------------- 
                                 \/                 2
(a4−x4)(a+x)2a2−(−a+x)(−a2+x2)2+a2−(−a+x)(−a2+x2)22\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2} 
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))
Denominador racional [src] 
          _____________________                 _____________________            _____________________
     2   /    2      2                     2   /    2      2                2   /    2      2         
- 8*x *\/  - x  + 3*a  + 2*a*x  - 8*(a - x) *\/  - x  + 3*a  + 2*a*x  + 40*a *\/  - x  + 3*a  + 2*a*x 
------------------------------------------------------------------------------------------------------
                                             2       2                                                
                                       - 32*x  + 96*a  + 64*a*x
40a23a2+2ax−x2−8x23a2+2ax−x2−8(a−x)23a2+2ax−x296a2+64ax−32x2\frac{40 a^{2} \sqrt{3 a^{2} + 2 a x - x^{2}} - 8 x^{2} \sqrt{3 a^{2} + 2 a x - x^{2}} - 8 \left(a - x\right)^{2} \sqrt{3 a^{2} + 2 a x - x^{2}}}{96 a^{2} + 64 a x - 32 x^{2}} 
(-8*x^2*sqrt(-x^2 + 3*a^2 + 2*a*x) - 8*(a - x)^2*sqrt(-x^2 + 3*a^2 + 2*a*x) + 40*a^2*sqrt(-x^2 + 3*a^2 + 2*a*x))/(-32*x^2 + 96*a^2 + 64*a*x)
Compilar la expresión [src] 
      ______________________                                 
     /              /x   a\                                  
    /       (x - a)*|- - -|                                  
   /    2           \2   2/                  /  x   a\       
  /    a  - ---------------          (a + x)*|- - + -|       
\/                 2                         \  4   4/       
---------------------------- + ------------------------------
             2                         ______________________
                                      /              /x   a\ 
                                     /       (x - a)*|- - -| 
                                    /    2           \2   2/ 
                               2*  /    a  - --------------- 
                                 \/                 2
(a4−x4)(a+x)2a2−(−a+x)(−a2+x2)2+a2−(−a+x)(−a2+x2)22\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2} 
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))
Unión de expresiones racionales [src] 
         2      2                  
- (x - a)  + 4*a  + (a + x)*(a - x)
-----------------------------------
           ___________________     
          /          2      2      
      4*\/  - (x - a)  + 4*a
4a2−(−a+x)2+(a−x)(a+x)44a2−(−a+x)2\frac{4 a^{2} - \left(- a + x\right)^{2} + \left(a - x\right) \left(a + x\right)}{4 \sqrt{4 a^{2} - \left(- a + x\right)^{2}}} 
(-(x - a)^2 + 4*a^2 + (a + x)*(a - x))/(4*sqrt(-(x - a)^2 + 4*a^2))
Combinatoria [src] 
  -(a + x)*(x - 2*a)    
------------------------
    ____________________
2*\/ -(a + x)*(x - 3*a)
−(−2a+x)(a+x)2−(−3a+x)(a+x)- \frac{\left(- 2 a + x\right) \left(a + x\right)}{2 \sqrt{- \left(- 3 a + x\right) \left(a + x\right)}} 
-(a + x)*(x - 2*a)/(2*sqrt(-(a + x)*(x - 3*a)))
Respuesta numérica [src] 
0.5*(a^2 - 0.25*(x - a)^2)^0.5 + 0.5*(a^2 - 0.25*(x - a)^2)^(-0.5)*(a + x)*(0.25*a - 0.25*x)
0.5*(a^2 - 0.25*(x - a)^2)^0.5 + 0.5*(a^2 - 0.25*(x - a)^2)^(-0.5)*(a + x)*(0.25*a - 0.25*x)
Potencias [src] 
      ______________________                                 
     /              /x   a\                                  
    /       (x - a)*|- - -|                                  
   /    2           \2   2/                  /  x   a\       
  /    a  - ---------------          (a + x)*|- - + -|       
\/                 2                         \  4   4/       
---------------------------- + ------------------------------
             2                         ______________________
                                      /              /x   a\ 
                                     /       (x - a)*|- - -| 
                                    /    2           \2   2/ 
                               2*  /    a  - --------------- 
                                 \/                 2
(a4−x4)(a+x)2a2−(−a+x)(−a2+x2)2+a2−(−a+x)(−a2+x2)22\frac{\left(\frac{a}{4} - \frac{x}{4}\right) \left(a + x\right)}{2 \sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}} + \frac{\sqrt{a^{2} - \frac{\left(- a + x\right) \left(- \frac{a}{2} + \frac{x}{2}\right)}{2}}}{2} 
sqrt(a^2 - (x - a)*(x/2 - a/2)/2)/2 + (a + x)*(-x/4 + a/4)/(2*sqrt(a^2 - (x - a)*(x/2 - a/2)/2))
    © Sr Examen – Калькулятор