\frac{m_1c^2}{\sqrt{\displaystyle 1-\frac{v_1^2}{c^2}}}-m_1c^2+\frac{m_2c^2}{\sqrt{\displaystyle 1-\frac{v_2^2}{c^2}}}-m_2c^2=\frac{m_1c^2}{\sqrt{\displaystyle 1-\frac{v_1'^2}{c^2}}}-m_1c^2+\frac{m_2c^2}{\sqrt{\displaystyle 1-\frac{v_2'^2}{c^2}}}-m_2c^2,