Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cot(x/(y^(1/2)))*x/(2*(y^(3/2)))*((x/3)^(1/2))/(2*(x/3+1)^(1/2))
¿Cómo vas a descomponer esta cot(x/(y^(1/2)))*x/(2*(y^(3/2)))*((x/3)^(1/2))/(2*(x/3+1)^(1/2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ x \
cot|-----|*x
| ___| ___
\\/ y / / x
------------* / -
3/2 \/ 3
2*y
--------------------
_______
/ x
2* / - + 1
\/ 3
$$\frac{\sqrt{\frac{x}{3}} \frac{x \cot{\left(\frac{x}{\sqrt{y}} \right)}}{2 y^{\frac{3}{2}}}}{2 \sqrt{\frac{x}{3} + 1}}$$
(((cot(x/sqrt(y))*x)/((2*y^(3/2))))*sqrt(x/3))/((2*sqrt(x/3 + 1)))
Simplificación general
[src]
3/2 / x \
x *cot|-----|
| ___|
\\/ y /
----------------
3/2 _______
4*y *\/ 3 + x
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Denominador racional
[src]
____ / ___\
3/2 / 3 |x*\/ y |
x *\/ y *cot|-------|
\ y /
-------------------------
3 _______
4*y *\/ 3 + x
$$\frac{x^{\frac{3}{2}} \sqrt{y^{3}} \cot{\left(\frac{x \sqrt{y}}{y} \right)}}{4 y^{3} \sqrt{x + 3}}$$
x^(3/2)*sqrt(y^3)*cot(x*sqrt(y)/y)/(4*y^3*sqrt(3 + x))
Denominador común
[src]
3/2 / x \
x *cot|-----|
| ___|
\\/ y /
----------------
3/2 _______
4*y *\/ 3 + x
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Potencias
[src]
___ 3/2 / x \
\/ 3 *x *cot|-----|
| ___|
\\/ y /
---------------------
_______
3/2 / x
12*y * / 1 + -
\/ 3
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
sqrt(3)*x^(3/2)*cot(x/sqrt(y))/(12*y^(3/2)*sqrt(1 + x/3))
Unión de expresiones racionales
[src]
3/2 / x \
x *cot|-----|
| ___|
\\/ y /
----------------
3/2 _______
4*y *\/ 3 + x
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Combinatoria
[src]
3/2 / x \
x *cot|-----|
| ___|
\\/ y /
----------------
3/2 _______
4*y *\/ 3 + x
$$\frac{x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{4 y^{\frac{3}{2}} \sqrt{x + 3}}$$
x^(3/2)*cot(x/sqrt(y))/(4*y^(3/2)*sqrt(3 + x))
Compilar la expresión
[src]
___ 3/2 / x \
\/ 3 *x *cot|-----|
| ___|
\\/ y /
---------------------
_______
3/2 / x
12*y * / 1 + -
\/ 3
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
sqrt(3)*x^(3/2)*cot(x/sqrt(y))/(12*y^(3/2)*sqrt(1 + x/3))
Parte trigonométrica
[src]
___ 3/2 / x \
\/ 3 *x *csc|-----|
| ___|
\\/ y /
-----------------------------------
_______
3/2 / x /pi x \
12*y * / 1 + - *csc|-- - -----|
\/ 3 |2 ___|
\ \/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \csc{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \csc{\left(- \frac{x}{\sqrt{y}} + \frac{\pi}{2} \right)}}$$
___ 3/2 / pi x \
\/ 3 *x *sec|- -- + -----|
| 2 ___|
\ \/ y /
------------------------------
_______
3/2 / x / x \
12*y * / 1 + - *sec|-----|
\/ 3 | ___|
\\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \sec{\left(\frac{x}{\sqrt{y}} - \frac{\pi}{2} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sec{\left(\frac{x}{\sqrt{y}} \right)}}$$
___ 3/2
\/ 3 *x
------------------------------
_______
3/2 / x / x \
12*y * / 1 + - *tan|-----|
\/ 3 | ___|
\\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \tan{\left(\frac{x}{\sqrt{y}} \right)}}$$
___ 3/2 / x \
\/ 3 *x *csc|-----|
| ___|
\\/ y /
------------------------------
_______
3/2 / x / x \
12*y * / 1 + - *sec|-----|
\/ 3 | ___|
\\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \csc{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sec{\left(\frac{x}{\sqrt{y}} \right)}}$$
___ 3/2 / x \
\/ 3 *x *cos|-----|
| ___|
\\/ y /
------------------------------
_______
3/2 / x / x \
12*y * / 1 + - *sin|-----|
\/ 3 | ___|
\\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cos{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sin{\left(\frac{x}{\sqrt{y}} \right)}}$$
___ 3/2 / x \
\/ 3 *x *cos|-----|
| ___|
\\/ y /
-------------------------------------
_______
3/2 / x / pi x \
12*y * / 1 + - *cos|- -- + -----|
\/ 3 | 2 ___|
\ \/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cos{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \cos{\left(\frac{x}{\sqrt{y}} - \frac{\pi}{2} \right)}}$$
___ 3/2 / x \
\/ 3 *x *cot|-----|
| ___|
\\/ y /
---------------------
_______
3/2 / x
12*y * / 1 + -
\/ 3
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
___ 3/2 / x \
\/ 3 *x *cot|-----|
| ___|
\\/ y /
---------------------
_______
3/2 / x
12*y * / - + 1
\/ 3
$$\frac{\sqrt{3} x^{\frac{3}{2}} \cot{\left(\frac{x}{\sqrt{y}} \right)}}{12 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1}}$$
___ 3/2 / 2*x \
\/ 3 *x *sin|-----|
| ___|
\\/ y /
-------------------------------
_______
3/2 / x 2/ x \
24*y * / 1 + - *sin |-----|
\/ 3 | ___|
\\/ y /
$$\frac{\sqrt{3} x^{\frac{3}{2}} \sin{\left(\frac{2 x}{\sqrt{y}} \right)}}{24 y^{\frac{3}{2}} \sqrt{\frac{x}{3} + 1} \sin^{2}{\left(\frac{x}{\sqrt{y}} \right)}}$$
sqrt(3)*x^(3/2)*sin(2*x/sqrt(y))/(24*y^(3/2)*sqrt(1 + x/3)*sin(x/sqrt(y))^2)
Respuesta numérica
[src]
0.144337567297406*x^1.5*y^(-1.5)*(1.0 + 0.333333333333333*x)^(-0.5)*cot(x/sqrt(y))
0.144337567297406*x^1.5*y^(-1.5)*(1.0 + 0.333333333333333*x)^(-0.5)*cot(x/sqrt(y))