Solve for A (complex solution)
\left\{\begin{matrix}A=-\frac{By^{2}-1}{x^{2}}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&B=\frac{1}{y^{2}}\text{ and }y\neq 0\text{ and }x=0\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=-\frac{Ax^{2}-1}{y^{2}}\text{, }&y\neq 0\\B\in \mathrm{C}\text{, }&A=\frac{1}{x^{2}}\text{ and }x\neq 0\text{ and }y=0\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=-\frac{By^{2}-1}{x^{2}}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&B=\frac{1}{y^{2}}\text{ and }y\neq 0\text{ and }x=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-\frac{Ax^{2}-1}{y^{2}}\text{, }&y\neq 0\\B\in \mathrm{R}\text{, }&A=\frac{1}{x^{2}}\text{ and }x\neq 0\text{ and }y=0\end{matrix}\right.
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Ax^{2}=1-By^{2}
Subtract By^{2} from both sides.
Ax^{2}=-By^{2}+1
Reorder the terms.
x^{2}A=1-By^{2}
The equation is in standard form.
\frac{x^{2}A}{x^{2}}=\frac{1-By^{2}}{x^{2}}
Divide both sides by x^{2}.
A=\frac{1-By^{2}}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
By^{2}=1-Ax^{2}
Subtract Ax^{2} from both sides.
By^{2}=-Ax^{2}+1
Reorder the terms.
y^{2}B=1-Ax^{2}
The equation is in standard form.
\frac{y^{2}B}{y^{2}}=\frac{1-Ax^{2}}{y^{2}}
Divide both sides by y^{2}.
B=\frac{1-Ax^{2}}{y^{2}}
Dividing by y^{2} undoes the multiplication by y^{2}.
Ax^{2}=1-By^{2}
Subtract By^{2} from both sides.
Ax^{2}=-By^{2}+1
Reorder the terms.
x^{2}A=1-By^{2}
The equation is in standard form.
\frac{x^{2}A}{x^{2}}=\frac{1-By^{2}}{x^{2}}
Divide both sides by x^{2}.
A=\frac{1-By^{2}}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
By^{2}=1-Ax^{2}
Subtract Ax^{2} from both sides.
By^{2}=-Ax^{2}+1
Reorder the terms.
y^{2}B=1-Ax^{2}
The equation is in standard form.
\frac{y^{2}B}{y^{2}}=\frac{1-Ax^{2}}{y^{2}}
Divide both sides by y^{2}.
B=\frac{1-Ax^{2}}{y^{2}}
Dividing by y^{2} undoes the multiplication by y^{2}.
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