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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(1-((1-x*x)*(n0*n0)/(n1*n1)))

¿Cómo vas a descomponer esta sqrt(1-((1-x*x)*(n0*n0)/(n1*n1))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    _____________________
   /     (1 - x*x)*n0*n0 
  /  1 - --------------- 
\/            n1*n1
$$\sqrt{- \frac{n_{0} n_{0} \left(- x x + 1\right)}{n_{1} n_{1}} + 1}$$ 
sqrt(1 - (1 - x*x)*(n0*n0)/(n1*n1))
Simplificación general [src] 
      ____________________
     /   2     2 /     2\ 
    /  n1  - n0 *\1 - x / 
   /   ------------------ 
  /             2         
\/            n1
$$\sqrt{\frac{- n_{0}^{2} \left(1 - x^{2}\right) + n_{1}^{2}}{n_{1}^{2}}}$$ 
sqrt((n1^2 - n0^2*(1 - x^2))/n1^2)
Descomposición de una fracción [src] 
sqrt(1 - n0^2/n1^2 + n0^2*x^2/n1^2)
$$\sqrt{\frac{n_{0}^{2} x^{2}}{n_{1}^{2}} - \frac{n_{0}^{2}}{n_{1}^{2}} + 1}$$ 
      __________________
     /       2     2  2 
    /      n0    n0 *x  
   /   1 - --- + ------ 
  /          2      2   
\/         n1     n1
Respuesta numérica [src] 
(1.0 - n0^2*(1.0 - x^2)/n1^2)^0.5
(1.0 - n0^2*(1.0 - x^2)/n1^2)^0.5
Abrimos la expresión [src] 
      ___________________
     /       2           
    /      n0 *(1 - x*x) 
   /   1 - ------------- 
  /               2      
\/              n1
$$\sqrt{- \frac{n_{0}^{2} \left(- x x + 1\right)}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2*(1 - x*x)/n1^2)
Parte trigonométrica [src] 
      __________________
     /       2 /     2\ 
    /      n0 *\1 - x / 
   /   1 - ------------ 
  /              2      
\/             n1
$$\sqrt{- \frac{n_{0}^{2} \left(1 - x^{2}\right)}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2*(1 - x^2)/n1^2)
Denominador común [src] 
      __________________
     /       2     2  2 
    /      n0    n0 *x  
   /   1 - --- + ------ 
  /          2      2   
\/         n1     n1
$$\sqrt{\frac{n_{0}^{2} x^{2}}{n_{1}^{2}} - \frac{n_{0}^{2}}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2/n1^2 + n0^2*x^2/n1^2)
Unión de expresiones racionales [src] 
      ____________________
     /   2     2 /     2\ 
    /  n1  - n0 *\1 - x / 
   /   ------------------ 
  /             2         
\/            n1
$$\sqrt{\frac{- n_{0}^{2} \left(1 - x^{2}\right) + n_{1}^{2}}{n_{1}^{2}}}$$ 
sqrt((n1^2 - n0^2*(1 - x^2))/n1^2)
Denominador racional [src] 
      ____________________
     /   2     2     2  2 
    /  n1  - n0  + n0 *x  
   /   ------------------ 
  /             2         
\/            n1
$$\sqrt{\frac{n_{0}^{2} x^{2} - n_{0}^{2} + n_{1}^{2}}{n_{1}^{2}}}$$ 
sqrt((n1^2 - n0^2 + n0^2*x^2)/n1^2)
Potencias [src] 
      ___________________
     /       2 /      2\ 
    /      n0 *\-1 + x / 
   /   1 + ------------- 
  /               2      
\/              n1
$$\sqrt{\frac{n_{0}^{2} \left(x^{2} - 1\right)}{n_{1}^{2}} + 1}$$ 
      __________________
     /       2 /     2\ 
    /      n0 *\1 - x / 
   /   1 - ------------ 
  /              2      
\/             n1
$$\sqrt{- \frac{n_{0}^{2} \left(1 - x^{2}\right)}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2*(1 - x^2)/n1^2)
Compilar la expresión [src] 
      __________________
     /       2 /     2\ 
    /      n0 *\1 - x / 
   /   1 - ------------ 
  /              2      
\/             n1
$$\sqrt{- \frac{n_{0}^{2} \left(1 - x^{2}\right)}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2*(1 - x^2)/n1^2)
Combinatoria [src] 
      __________________
     /       2     2  2 
    /      n0    n0 *x  
   /   1 - --- + ------ 
  /          2      2   
\/         n1     n1
$$\sqrt{\frac{n_{0}^{2} x^{2}}{n_{1}^{2}} - \frac{n_{0}^{2}}{n_{1}^{2}} + 1}$$ 
sqrt(1 - n0^2/n1^2 + n0^2*x^2/n1^2)
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