Solve for u (complex solution)
\left\{\begin{matrix}u=\frac{v}{x+y}\text{, }&x\neq -y\\u\in \mathrm{C}\text{, }&v=0\text{ and }x=-y\end{matrix}\right.
Solve for u
\left\{\begin{matrix}u=\frac{v}{x+y}\text{, }&x\neq -y\\u\in \mathrm{R}\text{, }&v=0\text{ and }x=-y\end{matrix}\right.
Solve for v
v=u\left(x+y\right)
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v=ux+uy
Use the distributive property to multiply u by x+y.
ux+uy=v
Swap sides so that all variable terms are on the left hand side.
\left(x+y\right)u=v
Combine all terms containing u.
\frac{\left(x+y\right)u}{x+y}=\frac{v}{x+y}
Divide both sides by x+y.
u=\frac{v}{x+y}
Dividing by x+y undoes the multiplication by x+y.
v=ux+uy
Use the distributive property to multiply u by x+y.
ux+uy=v
Swap sides so that all variable terms are on the left hand side.
\left(x+y\right)u=v
Combine all terms containing u.
\frac{\left(x+y\right)u}{x+y}=\frac{v}{x+y}
Divide both sides by x+y.
u=\frac{v}{x+y}
Dividing by x+y undoes the multiplication by x+y.
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