Solve for Q
Q=-\frac{x^{3}}{3}-\frac{x^{2}}{6}+\frac{x}{6}+\frac{1}{2}-\frac{1}{3x}
x\neq 0
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-3x+2x^{4}+6Qx=x^{2}-2-x^{3}
Subtract x^{3} from both sides.
2x^{4}+6Qx=x^{2}-2-x^{3}+3x
Add 3x to both sides.
6Qx=x^{2}-2-x^{3}+3x-2x^{4}
Subtract 2x^{4} from both sides.
6xQ=-2x^{4}-x^{3}+x^{2}+3x-2
The equation is in standard form.
\frac{6xQ}{6x}=\frac{-2x^{4}-x^{3}+x^{2}+3x-2}{6x}
Divide both sides by 6x.
Q=\frac{-2x^{4}-x^{3}+x^{2}+3x-2}{6x}
Dividing by 6x undoes the multiplication by 6x.
Q=-\frac{x^{3}}{3}-\frac{x^{2}}{6}+\frac{x}{6}+\frac{1}{2}-\frac{1}{3x}
Divide x^{2}-2-x^{3}+3x-2x^{4} by 6x.
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