Solve for W
\left\{\begin{matrix}W=\frac{Q\left(\gamma -1\right)}{\gamma -n}\text{, }&\gamma \neq n\text{ and }\gamma \neq 1\\W\in \mathrm{R}\text{, }&Q=0\text{ and }n=\gamma \text{ and }\gamma \neq 1\end{matrix}\right.
Solve for Q
Q=-\frac{W\left(n-\gamma \right)}{\gamma -1}
\gamma \neq 1
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Q\left(\gamma -1\right)=\left(\gamma -n\right)W
Multiply both sides of the equation by \gamma -1.
Q\gamma -Q=\left(\gamma -n\right)W
Use the distributive property to multiply Q by \gamma -1.
Q\gamma -Q=\gamma W-nW
Use the distributive property to multiply \gamma -n by W.
\gamma W-nW=Q\gamma -Q
Swap sides so that all variable terms are on the left hand side.
\left(\gamma -n\right)W=Q\gamma -Q
Combine all terms containing W.
\frac{\left(\gamma -n\right)W}{\gamma -n}=\frac{Q\left(\gamma -1\right)}{\gamma -n}
Divide both sides by \gamma -n.
W=\frac{Q\left(\gamma -1\right)}{\gamma -n}
Dividing by \gamma -n undoes the multiplication by \gamma -n.
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