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¿Cómo vas a descomponer esta asin(4/x)/x-4*log(x)/(x^2*sqrt(1-16/x^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$- \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}} + \frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Simplificación general [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$\frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x} - \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Respuesta numérica [src]
asin(4/x)/x - 1.0*(0.0625 - 1/x^2)^(-0.5)*log(x)/x^2
asin(4/x)/x - 1.0*(0.0625 - 1/x^2)^(-0.5)*log(x)/x^2
Combinatoria [src]
                   ________        
                  /     16      /4\
-4*log(x) + x*   /  1 - -- *asin|-|
                /        2      \x/
              \/        x          
-----------------------------------
            ___________________    
      2    /  /    4\ /     4\     
     x *  /  -|1 + -|*|-1 + -|     
        \/    \    x/ \     x/     
$$\frac{x \sqrt{1 - \frac{16}{x^{2}}} \operatorname{asin}{\left(\frac{4}{x} \right)} - 4 \log{\left(x \right)}}{x^{2} \sqrt{- \left(-1 + \frac{4}{x}\right) \left(1 + \frac{4}{x}\right)}}$$
(-4*log(x) + x*sqrt(1 - 16/x^2)*asin(4/x))/(x^2*sqrt(-(1 + 4/x)*(-1 + 4/x)))
Denominador común [src]
                   ________        
                  /     16      /4\
-4*log(x) + x*   /  1 - -- *asin|-|
                /        2      \x/
              \/        x          
-----------------------------------
                  ________         
           2     /     16          
          x *   /  1 - --          
               /        2          
             \/        x           
$$\frac{x \sqrt{1 - \frac{16}{x^{2}}} \operatorname{asin}{\left(\frac{4}{x} \right)} - 4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
(-4*log(x) + x*sqrt(1 - 16/x^2)*asin(4/x))/(x^2*sqrt(1 - 16/x^2))
Potencias [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$\frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x} - \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Denominador racional [src]
                      ________        
               2     /     16      /4\
-4*x*log(x) + x *   /  1 - -- *asin|-|
                   /        2      \x/
                 \/        x          
--------------------------------------
                   ________           
            3     /     16            
           x *   /  1 - --            
                /        2            
              \/        x             
$$\frac{x^{2} \sqrt{1 - \frac{16}{x^{2}}} \operatorname{asin}{\left(\frac{4}{x} \right)} - 4 x \log{\left(x \right)}}{x^{3} \sqrt{1 - \frac{16}{x^{2}}}}$$
(-4*x*log(x) + x^2*sqrt(1 - 16/x^2)*asin(4/x))/(x^3*sqrt(1 - 16/x^2))
Parte trigonométrica [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$\frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x} - \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Abrimos la expresión [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$\frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x} - \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Compilar la expresión [src]
    /4\                   
asin|-|                   
    \x/       4*log(x)    
------- - ----------------
   x              ________
           2     /     16 
          x *   /  1 - -- 
               /        2 
             \/        x  
$$\frac{\operatorname{asin}{\left(\frac{4}{x} \right)}}{x} - \frac{4 \log{\left(x \right)}}{x^{2} \sqrt{1 - \frac{16}{x^{2}}}}$$
asin(4/x)/x - 4*log(x)/(x^2*sqrt(1 - 16/x^2))
Unión de expresiones racionales [src]
                    __________        
                   /        2         
                  /  -16 + x       /4\
-4*log(x) + x*   /   -------- *asin|-|
                /        2         \x/
              \/        x             
--------------------------------------
                  __________          
                 /        2           
          2     /  -16 + x            
         x *   /   --------           
              /        2              
            \/        x               
$$\frac{x \sqrt{\frac{x^{2} - 16}{x^{2}}} \operatorname{asin}{\left(\frac{4}{x} \right)} - 4 \log{\left(x \right)}}{x^{2} \sqrt{\frac{x^{2} - 16}{x^{2}}}}$$
(-4*log(x) + x*sqrt((-16 + x^2)/x^2)*asin(4/x))/(x^2*sqrt((-16 + x^2)/x^2))