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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(log((x-1)/(x+5)))/sqrt(-log(10)+log(31))

¿Cómo vas a descomponer esta sqrt(log((x-1)/(x+5)))/sqrt(-log(10)+log(31)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       ____________   
      /    /x - 1\    
     /  log|-----|    
   \/      \x + 5/    
----------------------
  ____________________
\/ -log(10) + log(31)
log⁡(x−1x+5)−log⁡(10)+log⁡(31)\frac{\sqrt{\log{\left(\frac{x - 1}{x + 5} \right)}}}{\sqrt{- \log{\left(10 \right)} + \log{\left(31 \right)}}} 
sqrt(log((x - 1)/(x + 5)))/sqrt(-log(10) + log(31))
Simplificación general [src] 
    _____________
   /    /-1 + x\ 
  /  log|------| 
\/      \5 + x / 
-----------------
      _________  
     /    /31\   
    /  log|--|   
  \/      \10/
log⁡(x−1x+5)log⁡(3110)\frac{\sqrt{\log{\left(\frac{x - 1}{x + 5} \right)}}}{\sqrt{\log{\left(\frac{31}{10} \right)}}} 
sqrt(log((-1 + x)/(5 + x)))/sqrt(log(31/10))
Respuesta numérica [src] 
0.940137784603288*log((x - 1)/(x + 5))^0.5
0.940137784603288*log((x - 1)/(x + 5))^0.5
Denominador común [src] 
    ______________________
   /    /    1       x  \ 
  /  log|- ----- + -----| 
\/      \  5 + x   5 + x/ 
--------------------------
    ____________________  
  \/ -log(10) + log(31)
log⁡(xx+5−1x+5)−log⁡(10)+log⁡(31)\frac{\sqrt{\log{\left(\frac{x}{x + 5} - \frac{1}{x + 5} \right)}}}{\sqrt{- \log{\left(10 \right)} + \log{\left(31 \right)}}} 
sqrt(log(-1/(5 + x) + x/(5 + x)))/sqrt(-log(10) + log(31))
Combinatoria [src] 
    ______________________
   /    /    1       x  \ 
  /  log|- ----- + -----| 
\/      \  5 + x   5 + x/ 
--------------------------
    ____________________  
  \/ -log(10) + log(31)
log⁡(xx+5−1x+5)−log⁡(10)+log⁡(31)\frac{\sqrt{\log{\left(\frac{x}{x + 5} - \frac{1}{x + 5} \right)}}}{\sqrt{- \log{\left(10 \right)} + \log{\left(31 \right)}}} 
sqrt(log(-1/(5 + x) + x/(5 + x)))/sqrt(-log(10) + log(31))
Denominador racional [src] 
                            _____________ 
   ____________________    /    /-1 + x\  
-\/ -log(10) + log(31) *  /  log|------|  
                        \/      \x + 5 /  
------------------------------------------
            -log(31) + log(10)
−−log⁡(10)+log⁡(31)log⁡(x−1x+5)−log⁡(31)+log⁡(10)- \frac{\sqrt{- \log{\left(10 \right)} + \log{\left(31 \right)}} \sqrt{\log{\left(\frac{x - 1}{x + 5} \right)}}}{- \log{\left(31 \right)} + \log{\left(10 \right)}} 
-sqrt(-log(10) + log(31))*sqrt(log((-1 + x)/(x + 5)))/(-log(31) + log(10))
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