Solve for y (complex solution)
\left\{\begin{matrix}y=\frac{1}{3x^{2}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=\frac{1}{3x^{2}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{3}y^{-\frac{1}{2}}}{3}\text{; }x=\frac{\sqrt{3}y^{-\frac{1}{2}}}{3}\text{, }&y\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{\frac{3}{y}}}{3}\text{; }x=-\frac{\sqrt{\frac{3}{y}}}{3}\text{, }&y>0\end{matrix}\right.
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3x^{4}y=x^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{3x^{4}y}{3x^{4}}=\frac{x^{2}}{3x^{4}}
Divide both sides by 3x^{4}.
y=\frac{x^{2}}{3x^{4}}
Dividing by 3x^{4} undoes the multiplication by 3x^{4}.
y=\frac{1}{3x^{2}}
Divide x^{2} by 3x^{4}.
3x^{4}y=x^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{3x^{4}y}{3x^{4}}=\frac{x^{2}}{3x^{4}}
Divide both sides by 3x^{4}.
y=\frac{x^{2}}{3x^{4}}
Dividing by 3x^{4} undoes the multiplication by 3x^{4}.
y=\frac{1}{3x^{2}}
Divide x^{2} by 3x^{4}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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