Sr Examen

Otras calculadoras

¿Cómo vas a descomponer esta sqrt(2)/(4*x^(3/2)*sqrt(1-1/(2*x))*acos(1/(sqrt(2*x)))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                ___               
              \/ 2                
----------------------------------
           _________              
   3/2    /      1       /   1   \
4*x   *  /  1 - --- *acos|-------|
       \/       2*x      |  _____|
                         \\/ 2*x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{1}{\sqrt{2 x}} \right)}}$$
sqrt(2)/((((4*x^(3/2))*sqrt(1 - 1/(2*x)))*acos(1/(sqrt(2*x)))))
Simplificación general [src]
               1                
--------------------------------
           _______     /   ___ \
   3/2    /     1      | \/ 2  |
2*x   *  /  2 - - *acos|-------|
       \/       x      |    ___|
                       \2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{2 - \frac{1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt(2 - 1/x)*acos(sqrt(2)/(2*sqrt(x))))
Respuesta numérica [src]
0.353553390593274*x^(-1.5)*(1.0 - 0.5/x)^(-0.5)/acos(1/(sqrt(2*x)))
0.353553390593274*x^(-1.5)*(1.0 - 0.5/x)^(-0.5)/acos(1/(sqrt(2*x)))
Abrimos la expresión [src]
                ___               
              \/ 2                
----------------------------------
           _________     /   ___ \
   3/2    /      1       | \/ 2  |
4*x   *  /  1 - --- *acos|-------|
       \/       2*x      |    ___|
                         \2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))
Combinatoria [src]
               1                
--------------------------------
           _______     /   ___ \
   3/2    /     1      | \/ 2  |
2*x   *  /  2 - - *acos|-------|
       \/       x      |    ___|
                       \2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{2 - \frac{1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt(2 - 1/x)*acos(sqrt(2)/(2*sqrt(x))))
Denominador racional [src]
                    ____            
             ___   /  3             
           \/ 2 *\/  x              
------------------------------------
         _________     /  ___   ___\
   3    /      1       |\/ 2 *\/ x |
4*x *  /  1 - --- *acos|-----------|
     \/       2*x      \    2*x    /
$$\frac{\sqrt{2} \sqrt{x^{3}}}{4 x^{3} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2} \sqrt{x}}{2 x} \right)}}$$
sqrt(2)*sqrt(x^3)/(4*x^3*sqrt(1 - 1/(2*x))*acos(sqrt(2)*sqrt(x)/(2*x)))
Denominador común [src]
                ___               
              \/ 2                
----------------------------------
           _________     /   ___ \
   3/2    /      1       | \/ 2  |
4*x   *  /  1 - --- *acos|-------|
       \/       2*x      |    ___|
                         \2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))
Potencias [src]
                ___               
              \/ 2                
----------------------------------
           _________     /   ___ \
   3/2    /      1       | \/ 2  |
4*x   *  /  1 - --- *acos|-------|
       \/       2*x      |    ___|
                         \2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))
Unión de expresiones racionales [src]
                 1                 
-----------------------------------
           __________     /   ___ \
   3/2    / -1 + 2*x      | \/ 2  |
2*x   *  /  -------- *acos|-------|
       \/      x          |    ___|
                          \2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{\frac{2 x - 1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt((-1 + 2*x)/x)*acos(sqrt(2)/(2*sqrt(x))))
Parte trigonométrica [src]
                ___               
              \/ 2                
----------------------------------
           _________     /   ___ \
   3/2    /      1       | \/ 2  |
4*x   *  /  1 - --- *acos|-------|
       \/       2*x      |    ___|
                         \2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))