Why do text books not just write t_p_x*mu_x+t as minus lí_x+t/l_x since t_p_x is l_x+t/l_x and mu_x+t is minus lí_x+t/l_x+t meaning that t_p_x*mu_x+t equals (l_x+t/l_x)*( minus lí_x+t/l_x+t) which equals minus lí_x+t/l_x?

One does wonder!