Derivation of Physics Equation

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How do we derive these laws: (most of the time, the numbers are subscript)
v'2 = v1 * ( (2 * m) / (m1 + m2) ) + v2 * ( (m2-m1) / (m1+m2) )
&
v'1 = v1 * ( (m1-m2) / (m1+m2) ) + v2 * ( (2 * m2) / (m1 + m2) )

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