Solve v1f= (m1 x v1 + m^2 x v^2)/ m1

Evaluate

v \times 1 \times f = \frac{m \times 1 \times xv \times 1 + m ^{2} x v ^{2}}{m} \times 1

Multiply the terms

v f = \frac{m \times 1 \times xv \times 1 + m ^{2} x v ^{2}}{m} \times 1

Simplify

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v f = xv + x v^{2} m

Rewrite the expression

v f = vx + v^{2} m x

Swap the sides of the equation

vx + v^{2} m x = v f

Simplify

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(v + m v^{2}) x = v f

Divide both sides

\frac{( v + m v ^{2} ) x}{v + m v ^{2}} = \frac{v f}{v + m v ^{2}}

Divide the numbers

x = \frac{v f}{v + m v ^{2}}

Solution

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x = \frac{f}{1 + m v}

V1f= (m1 x v1 + m^2 x v^2)/ m1