You found the correct LCD. You probably made a mistake when rewriting the first fraction. You may have thought that $\displaystyle{\left({y}+{2}\right)}{\left({y}+{7}\right)}\usepackage{cmbright}\Huge\$ was equal to $\displaystyle{{y}}^{{2}}+{14}\usepackage{cmbright}\Huge\$ . Remember to use FOIL when multiplying binomials.