Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y^{2}}{z}-1\text{, }&z\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y^{2}}{z}-1\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.
Solve for y (complex solution)
y=-\sqrt{z\left(x+1\right)}
y=\sqrt{z\left(x+1\right)}
Solve for y
y=\sqrt{z\left(x+1\right)}
y=-\sqrt{z\left(x+1\right)}\text{, }\left(z\geq 0\text{ and }x\geq -1\right)\text{ or }\left(x\leq -1\text{ and }z\leq 0\right)
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xz=y^{2}-z
Swap sides so that all variable terms are on the left hand side.
zx=y^{2}-z
The equation is in standard form.
\frac{zx}{z}=\frac{y^{2}-z}{z}
Divide both sides by z.
x=\frac{y^{2}-z}{z}
Dividing by z undoes the multiplication by z.
x=\frac{y^{2}}{z}-1
Divide y^{2}-z by z.
xz=y^{2}-z
Swap sides so that all variable terms are on the left hand side.
zx=y^{2}-z
The equation is in standard form.
\frac{zx}{z}=\frac{y^{2}-z}{z}
Divide both sides by z.
x=\frac{y^{2}-z}{z}
Dividing by z undoes the multiplication by z.
x=\frac{y^{2}}{z}-1
Divide y^{2}-z by z.
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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