Solve for P
\left\{\begin{matrix}P=-\frac{\left(1-x\right)\left(x^{2}+1\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\P\in \mathrm{R}\text{, }&x=1\text{ and }f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=-\frac{\left(1-x\right)\left(x^{2}+1\right)}{Px}\text{, }&x\neq 0\text{ and }P\neq 0\\f\in \mathrm{R}\text{, }&x=1\text{ and }P=0\end{matrix}\right.
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fxP=x^{3}-x^{2}+x-1
The equation is in standard form.
\frac{fxP}{fx}=\frac{\left(x-1\right)\left(x^{2}+1\right)}{fx}
Divide both sides by fx.
P=\frac{\left(x-1\right)\left(x^{2}+1\right)}{fx}
Dividing by fx undoes the multiplication by fx.
Pxf=x^{3}-x^{2}+x-1
The equation is in standard form.
\frac{Pxf}{Px}=\frac{\left(x-1\right)\left(x^{2}+1\right)}{Px}
Divide both sides by Px.
f=\frac{\left(x-1\right)\left(x^{2}+1\right)}{Px}
Dividing by Px undoes the multiplication by Px.
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