[tex]a(m_1+m_2) = m_2g-m_1g\mu \ \ /:(m_1+m_2)\\\\a(m_1+m_2) = g(m_2-m_1\mu) \ \ /:(m_1+m_2)\\\\a = \frac{g(m_2-m_1\mu)}{m_1+m_2}[/tex]
[tex]N = m_1(a+g\mu) = m_1(\dfrac{m_2g-m_1g\mu}{m_1+m_2}+g\mu)=m_1[\dfrac{m_2g-m_1g\mu+g\mu(m_1+m_2)}{m_1+m_2}]=\\\\=m_1(\dfrac{m_2g-m_1g\mu+m_1g\mu+m_2g\mu}{m_1+m_2})=m_1(\dfrac{m_2g+m_2g\mu}{m_1+m_2})=m_1[\dfrac{m_2(g+g\mu)}{m_1+m_2}]=\\\\=\dfrac{m_1m_2g(1+\mu)}{m_1+m_2}=\dfrac{m_1m_2g}{m_1+m_2}(1+\mu)[/tex]
