Solve for x (complex solution)
x=\frac{1}{y^{2}+2y-10}
y\neq \sqrt{11}-1\text{ and }y\neq -\left(\sqrt{11}+1\right)
Solve for x
x=\frac{1}{y^{2}+2y-10}
y\neq \sqrt{11}-1\text{ and }y\neq -\sqrt{11}-1
Solve for y (complex solution)
y=\frac{\sqrt{11x^{2}+x}}{x}-1
y=-\frac{\sqrt{11x^{2}+x}}{x}-1\text{, }x\neq 0
Solve for y
y=\frac{\sqrt{11x^{2}+x}}{x}-1
y=-\frac{\sqrt{11x^{2}+x}}{x}-1\text{, }x>0\text{ or }x\leq -\frac{1}{11}
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xy^{2}+2xy-10x=1
Add 1 to both sides. Anything plus zero gives itself.
\left(y^{2}+2y-10\right)x=1
Combine all terms containing x.
\frac{\left(y^{2}+2y-10\right)x}{y^{2}+2y-10}=\frac{1}{y^{2}+2y-10}
Divide both sides by y^{2}+2y-10.
x=\frac{1}{y^{2}+2y-10}
Dividing by y^{2}+2y-10 undoes the multiplication by y^{2}+2y-10.
xy^{2}+2xy-10x=1
Add 1 to both sides. Anything plus zero gives itself.
\left(y^{2}+2y-10\right)x=1
Combine all terms containing x.
\frac{\left(y^{2}+2y-10\right)x}{y^{2}+2y-10}=\frac{1}{y^{2}+2y-10}
Divide both sides by y^{2}+2y-10.
x=\frac{1}{y^{2}+2y-10}
Dividing by y^{2}+2y-10 undoes the multiplication by y^{2}+2y-10.
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