Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))
¿Cómo vas a descomponer esta y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2))))))) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2*x \ | 1 + --------------| | _________| | / 2 2 | | 2*\/ x + y | y*|y + ------------------| | _________ | | / 2 2 | \ x + \/ x + y /
$$y \left(y + \frac{\frac{2 x}{2 \sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$
y*(y + (1 + (2*x)/((2*sqrt(x^2 + y^2))))/(x + sqrt(x^2 + y^2)))
Simplificación general
[src]
2 y
y + ------------
_________
/ 2 2
\/ x + y
$$y^{2} + \frac{y}{\sqrt{x^{2} + y^{2}}}$$
y^2 + y/sqrt(x^2 + y^2)
Respuesta numérica
[src]
y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5))
y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5))
Denominador racional
[src]
3/2 _________
2 / 2 2\ 2 / 2 2
2*y + 2*y*\x + y / - 2*y*x *\/ x + y
---------------------------------------------
_________
/ 2 2
2*y*\/ x + y
$$\frac{- 2 x^{2} y \sqrt{x^{2} + y^{2}} + 2 y^{2} + 2 y \left(x^{2} + y^{2}\right)^{\frac{3}{2}}}{2 y \sqrt{x^{2} + y^{2}}}$$
(2*y^2 + 2*y*(x^2 + y^2)^(3/2) - 2*y*x^2*sqrt(x^2 + y^2))/(2*y*sqrt(x^2 + y^2))
Compilar la expresión
[src]
/ x \ | 1 + ------------| | _________| | / 2 2 | | \/ x + y | y*|y + ----------------| | _________| | / 2 2 | \ x + \/ x + y /
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
Combinatoria
[src]
/ _________\
| / 2 2 |
y*\1 + y*\/ x + y /
----------------------
_________
/ 2 2
\/ x + y
$$\frac{y \left(y \sqrt{x^{2} + y^{2}} + 1\right)}{\sqrt{x^{2} + y^{2}}}$$
y*(1 + y*sqrt(x^2 + y^2))/sqrt(x^2 + y^2)
Parte trigonométrica
[src]
/ x \ | 1 + ------------| | _________| | / 2 2 | | \/ x + y | y*|y + ----------------| | _________| | / 2 2 | \ x + \/ x + y /
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))
Unión de expresiones racionales
[src]
/ _________\
| / 2 2 |
y*\1 + y*\/ x + y /
----------------------
_________
/ 2 2
\/ x + y
$$\frac{y \left(y \sqrt{x^{2} + y^{2}} + 1\right)}{\sqrt{x^{2} + y^{2}}}$$
y*(1 + y*sqrt(x^2 + y^2))/sqrt(x^2 + y^2)
Denominador común
[src]
_________
/ 2 2
2 x*y + y*\/ x + y
y + ------------------------
_________
2 2 / 2 2
x + y + x*\/ x + y
$$y^{2} + \frac{x y + y \sqrt{x^{2} + y^{2}}}{x^{2} + x \sqrt{x^{2} + y^{2}} + y^{2}}$$
y^2 + (x*y + y*sqrt(x^2 + y^2))/(x^2 + y^2 + x*sqrt(x^2 + y^2))
Potencias
[src]
/ x \ | 1 + ------------| | _________| | / 2 2 | | \/ x + y | y*|y + ----------------| | _________| | / 2 2 | \ x + \/ x + y /
$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$
y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2)))