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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2))

¿Cómo vas a descomponer esta sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   _________________                         
  /               2                          
\/  675 + 30*x - x       (15 + x)*(15 - x)   
-------------------- + ----------------------
         4                  _________________
                           /               2 
                       4*\/  675 + 30*x - x
(15−x)(x+15)4−x2+(30x+675)+−x2+(30x+675)4\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + \left(30 x + 675\right)}} + \frac{\sqrt{- x^{2} + \left(30 x + 675\right)}}{4} 
sqrt(675 + 30*x - x^2)/4 + ((15 + x)*(15 - x))/((4*sqrt(675 + 30*x - x^2)))
Simplificación general [src] 
          2           
   450 - x  + 15*x    
----------------------
     _________________
    /        2        
2*\/  675 - x  + 30*x
−x2+15x+4502−x2+30x+675\frac{- x^{2} + 15 x + 450}{2 \sqrt{- x^{2} + 30 x + 675}} 
(450 - x^2 + 15*x)/(2*sqrt(675 - x^2 + 30*x))
Compilar la expresión [src] 
   _________________                         
  /        2                                 
\/  675 - x  + 30*x      (15 + x)*(15 - x)   
-------------------- + ----------------------
         4                  _________________
                           /        2        
                       4*\/  675 - x  + 30*x
(15−x)(x+15)4−x2+30x+675+−x2+30x+6754\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4} 
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Respuesta numérica [src] 
6.49519052838329*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^0.5 + 0.00962250448649376*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^(-0.5)*(15.0 + x)*(15.0 - x)
6.49519052838329*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^0.5 + 0.00962250448649376*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^(-0.5)*(15.0 + x)*(15.0 - x)
Denominador racional [src] 
        _________________           _________________            _________________
       /        2              2   /        2                   /        2        
3600*\/  675 - x  + 30*x  - 8*x *\/  675 - x  + 30*x  + 120*x*\/  675 - x  + 30*x 
----------------------------------------------------------------------------------
                                          2                                       
                              10800 - 16*x  + 480*x
−8x2−x2+30x+675+120x−x2+30x+675+3600−x2+30x+675−16x2+480x+10800\frac{- 8 x^{2} \sqrt{- x^{2} + 30 x + 675} + 120 x \sqrt{- x^{2} + 30 x + 675} + 3600 \sqrt{- x^{2} + 30 x + 675}}{- 16 x^{2} + 480 x + 10800} 
(3600*sqrt(675 - x^2 + 30*x) - 8*x^2*sqrt(675 - x^2 + 30*x) + 120*x*sqrt(675 - x^2 + 30*x))/(10800 - 16*x^2 + 480*x)
Potencias [src] 
   _________________                         
  /        2                                 
\/  675 - x  + 30*x      (15 + x)*(15 - x)   
-------------------- + ----------------------
         4                  _________________
                           /        2        
                       4*\/  675 - x  + 30*x
(15−x)(x+15)4−x2+30x+675+−x2+30x+6754\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4} 
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Parte trigonométrica [src] 
   _________________                         
  /        2                                 
\/  675 - x  + 30*x      (15 + x)*(15 - x)   
-------------------- + ----------------------
         4                  _________________
                           /        2        
                       4*\/  675 - x  + 30*x
(15−x)(x+15)4−x2+30x+675+−x2+30x+6754\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4} 
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Denominador común [src] 
  /        2       \  
 -\-450 + x  - 15*x/  
----------------------
     _________________
    /        2        
2*\/  675 - x  + 30*x
−x2−15x−4502−x2+30x+675- \frac{x^{2} - 15 x - 450}{2 \sqrt{- x^{2} + 30 x + 675}} 
-(-450 + x^2 - 15*x)/(2*sqrt(675 - x^2 + 30*x))
Combinatoria [src] 
   -(-30 + x)*(15 + x)   
-------------------------
    _____________________
2*\/ -(-45 + x)*(15 + x)
−(x−30)(x+15)2−(x−45)(x+15)- \frac{\left(x - 30\right) \left(x + 15\right)}{2 \sqrt{- \left(x - 45\right) \left(x + 15\right)}} 
-(-30 + x)*(15 + x)/(2*sqrt(-(-45 + x)*(15 + x)))
Unión de expresiones racionales [src] 
       2                           
675 - x  + 30*x + (15 + x)*(15 - x)
-----------------------------------
            _________________      
           /        2              
       4*\/  675 - x  + 30*x
−x2+30x+(15−x)(x+15)+6754−x2+30x+675\frac{- x^{2} + 30 x + \left(15 - x\right) \left(x + 15\right) + 675}{4 \sqrt{- x^{2} + 30 x + 675}} 
(675 - x^2 + 30*x + (15 + x)*(15 - x))/(4*sqrt(675 - x^2 + 30*x))
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