Solve for s (complex solution)
\left\{\begin{matrix}s=\frac{tx\left(x+m\right)}{m}\text{, }&m\neq 0\text{ and }x\neq 0\text{ and }x\neq -m\\s\in \mathrm{C}\text{, }&t=0\text{ and }m=0\text{ and }x\neq 0\end{matrix}\right.
Solve for s
\left\{\begin{matrix}s=\frac{tx\left(x+m\right)}{m}\text{, }&m\neq 0\text{ and }x\neq 0\text{ and }x\neq -m\\s\in \mathrm{R}\text{, }&t=0\text{ and }m=0\text{ and }x\neq 0\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=-\frac{tx^{2}}{tx-s}\text{, }&x\neq 0\text{ and }s\neq 0\text{ and }s\neq tx\\m\neq -x\text{, }&x\neq 0\text{ and }s=0\text{ and }t=0\end{matrix}\right.
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\left(x+m\right)s=x\left(x+m\right)t+xs
Multiply both sides of the equation by x\left(x+m\right), the least common multiple of x,x+m.
xs+ms=x\left(x+m\right)t+xs
Use the distributive property to multiply x+m by s.
xs+ms=\left(x^{2}+xm\right)t+xs
Use the distributive property to multiply x by x+m.
xs+ms=x^{2}t+xmt+xs
Use the distributive property to multiply x^{2}+xm by t.
xs+ms-xs=x^{2}t+xmt
Subtract xs from both sides.
ms=x^{2}t+xmt
Combine xs and -xs to get 0.
ms=tx^{2}+mtx
The equation is in standard form.
\frac{ms}{m}=\frac{tx\left(x+m\right)}{m}
Divide both sides by m.
s=\frac{tx\left(x+m\right)}{m}
Dividing by m undoes the multiplication by m.
\left(x+m\right)s=x\left(x+m\right)t+xs
Multiply both sides of the equation by x\left(x+m\right), the least common multiple of x,x+m.
xs+ms=x\left(x+m\right)t+xs
Use the distributive property to multiply x+m by s.
xs+ms=\left(x^{2}+xm\right)t+xs
Use the distributive property to multiply x by x+m.
xs+ms=x^{2}t+xmt+xs
Use the distributive property to multiply x^{2}+xm by t.
xs+ms-xs=x^{2}t+xmt
Subtract xs from both sides.
ms=x^{2}t+xmt
Combine xs and -xs to get 0.
ms=tx^{2}+mtx
The equation is in standard form.
\frac{ms}{m}=\frac{tx\left(x+m\right)}{m}
Divide both sides by m.
s=\frac{tx\left(x+m\right)}{m}
Dividing by m undoes the multiplication by m.
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