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- La ecuación:
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Ecuación 5*x=32+x
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Ecuación 3*x^2+13*x-10=0
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Ecuación (2*x^2+7*x+3)/(x^2-9)=1
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Ecuación 3x=6
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -11*x-11*y=4
- 18*x-14*y=-2
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Expresiones idénticas
- z=(x+ tres *y)/(- tres *x+y)
- z es igual a (x más 3 multiplicar por y) dividir por ( menos 3 multiplicar por x más y)
- z es igual a (x más tres multiplicar por y) dividir por ( menos tres multiplicar por x más y)
- z=(x+3y)/(-3x+y)
- z=x+3y/-3x+y
- z=(x+3*y) dividir por (-3*x+y)
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Expresiones semejantes
- z=(x+3*y)/(-3*x-y)
- z=(x+3*y)/(3*x+y)
- z=(x-3*y)/(-3*x+y)
z=(x+3*y)/(-3*x+y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación:
$$z = \frac{x + 3 y}{- 3 x + y}$$
cambiamos:
$$z = - \frac{x + 3 y}{3 x - y}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
Sumamos los términos semejantes en el miembro derecho de la ecuación:
Obtenemos la respuesta: z = -(x + 3*y)/(-y + 3*x)
$$z = \frac{x + 3 y}{- 3 x + y}$$
cambiamos:
$$z = - \frac{x + 3 y}{3 x - y}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
z = -x-3*y-y+3*x
Sumamos los términos semejantes en el miembro derecho de la ecuación:
z = -(x + 3*y)/(-y + 3*x)
Obtenemos la respuesta: z = -(x + 3*y)/(-y + 3*x)
Gráfica
Respuesta rápida
[src]
/ (-re(y) + 3*re(x))*(3*im(y) + im(x)) (-3*im(x) + im(y))*(3*re(y) + re(x)) \ (-3*im(x) + im(y))*(3*im(y) + im(x)) (-re(y) + 3*re(x))*(3*re(y) + re(x))
z1 = I*|- ----------------------------------------- - -----------------------------------------| + ----------------------------------------- - -----------------------------------------
| 2 2 2 2| 2 2 2 2
\ (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) / (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x))
$$z_{1} = i \left(- \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}$$
z1 = i*(-(re(x) + 3*re(y))*(-3*im(x) + im(y))/((3*re(x) - re(y))^2 + (3*im(x) - im(y))^2) - (3*re(x) - re(y))*(im(x) + 3*im(y))/((3*re(x) - re(y))^2 + (3*im(x) - im(y))^2)) - (re(x) + 3*re(y))*(3*re(x) - re(y))/((3*re(x) - re(y))^2 + (3*im(x) - im(y))^2) + (-3*im(x) + im(y))*(im(x) + 3*im(y))/((3*re(x) - re(y))^2 + (3*im(x) - im(y))^2)
Suma y producto de raíces
[src]
suma
/ (-re(y) + 3*re(x))*(3*im(y) + im(x)) (-3*im(x) + im(y))*(3*re(y) + re(x)) \ (-3*im(x) + im(y))*(3*im(y) + im(x)) (-re(y) + 3*re(x))*(3*re(y) + re(x)) I*|- ----------------------------------------- - -----------------------------------------| + ----------------------------------------- - ----------------------------------------- | 2 2 2 2| 2 2 2 2 \ (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) / (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x))
$$i \left(- \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}$$
=
/ (-re(y) + 3*re(x))*(3*im(y) + im(x)) (-3*im(x) + im(y))*(3*re(y) + re(x)) \ (-3*im(x) + im(y))*(3*im(y) + im(x)) (-re(y) + 3*re(x))*(3*re(y) + re(x)) I*|- ----------------------------------------- - -----------------------------------------| + ----------------------------------------- - ----------------------------------------- | 2 2 2 2| 2 2 2 2 \ (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) / (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x))
$$i \left(- \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}$$
producto
/ (-re(y) + 3*re(x))*(3*im(y) + im(x)) (-3*im(x) + im(y))*(3*re(y) + re(x)) \ (-3*im(x) + im(y))*(3*im(y) + im(x)) (-re(y) + 3*re(x))*(3*re(y) + re(x)) I*|- ----------------------------------------- - -----------------------------------------| + ----------------------------------------- - ----------------------------------------- | 2 2 2 2| 2 2 2 2 \ (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) / (-im(y) + 3*im(x)) + (-re(y) + 3*re(x)) (-im(y) + 3*im(x)) + (-re(y) + 3*re(x))
$$i \left(- \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}$$
=
I*((-im(y) + 3*im(x))*(3*re(y) + re(x)) - (-re(y) + 3*re(x))*(3*im(y) + im(x))) - (-im(y) + 3*im(x))*(3*im(y) + im(x)) - (-re(y) + 3*re(x))*(3*re(y) + re(x))
-------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(-im(y) + 3*im(x)) + (-re(y) + 3*re(x))
$$\frac{i \left(\left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right) - \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right)\right) - \left(\operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right) - \left(\operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)}{\left(3 \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(y\right)}\right)^{2}}$$
(i*((-im(y) + 3*im(x))*(3*re(y) + re(x)) - (-re(y) + 3*re(x))*(3*im(y) + im(x))) - (-im(y) + 3*im(x))*(3*im(y) + im(x)) - (-re(y) + 3*re(x))*(3*re(y) + re(x)))/((-im(y) + 3*im(x))^2 + (-re(y) + 3*re(x))^2)