Solve for X
X=\frac{mv}{m+v}
v\neq 0\text{ and }m\neq 0\text{ and }m\neq -v
Solve for m
m=-\frac{Xv}{X-v}
v\neq 0\text{ and }X\neq 0\text{ and }X\neq v
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mv=Xv+Xm
Variable X cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Xmv, the least common multiple of X,m,v.
Xv+Xm=mv
Swap sides so that all variable terms are on the left hand side.
\left(v+m\right)X=mv
Combine all terms containing X.
\left(m+v\right)X=mv
The equation is in standard form.
\frac{\left(m+v\right)X}{m+v}=\frac{mv}{m+v}
Divide both sides by v+m.
X=\frac{mv}{m+v}
Dividing by v+m undoes the multiplication by v+m.
X=\frac{mv}{m+v}\text{, }X\neq 0
Variable X cannot be equal to 0.
mv=Xv+Xm
Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Xmv, the least common multiple of X,m,v.
mv-Xm=Xv
Subtract Xm from both sides.
\left(v-X\right)m=Xv
Combine all terms containing m.
\frac{\left(v-X\right)m}{v-X}=\frac{Xv}{v-X}
Divide both sides by v-X.
m=\frac{Xv}{v-X}
Dividing by v-X undoes the multiplication by v-X.
m=\frac{Xv}{v-X}\text{, }m\neq 0
Variable m cannot be equal to 0.
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