Solve for x
x=-\frac{6}{y\left(y^{2}-1\right)}
|y|\neq 1\text{ and }y\neq 0
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xy^{3}-xy=-6
Subtract 6 from both sides. Anything subtracted from zero gives its negation.
\left(y^{3}-y\right)x=-6
Combine all terms containing x.
\frac{\left(y^{3}-y\right)x}{y^{3}-y}=-\frac{6}{y^{3}-y}
Divide both sides by y^{3}-y.
x=-\frac{6}{y^{3}-y}
Dividing by y^{3}-y undoes the multiplication by y^{3}-y.
x=-\frac{6}{y\left(y^{2}-1\right)}
Divide -6 by y^{3}-y.
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