Solve for H
\left\{\begin{matrix}H=\frac{dw}{Tr}\text{, }&T\neq 0\text{ and }r\neq 0\\H\in \mathrm{R}\text{, }&\left(w=0\text{ and }T=0\right)\text{ or }\left(d=0\text{ and }T=0\right)\text{ or }\left(d=0\text{ and }r=0\text{ and }T\neq 0\right)\text{ or }\left(w=0\text{ and }r=0\text{ and }T\neq 0\right)\end{matrix}\right.
Solve for T
\left\{\begin{matrix}T=\frac{dw}{Hr}\text{, }&H\neq 0\text{ and }r\neq 0\\T\in \mathrm{R}\text{, }&\left(w=0\text{ and }H=0\right)\text{ or }\left(d=0\text{ and }H=0\right)\text{ or }\left(d=0\text{ and }r=0\text{ and }H\neq 0\right)\text{ or }\left(w=0\text{ and }r=0\text{ and }H\neq 0\right)\end{matrix}\right.
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rTH=wd
Swap sides so that all variable terms are on the left hand side.
TrH=dw
The equation is in standard form.
\frac{TrH}{Tr}=\frac{dw}{Tr}
Divide both sides by rT.
H=\frac{dw}{Tr}
Dividing by rT undoes the multiplication by rT.
rTH=wd
Swap sides so that all variable terms are on the left hand side.
HrT=dw
The equation is in standard form.
\frac{HrT}{Hr}=\frac{dw}{Hr}
Divide both sides by rH.
T=\frac{dw}{Hr}
Dividing by rH undoes the multiplication by rH.
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