[tex]\begin{gathered} \frac{2x-9}{x-7}+\frac{x}{2}=\frac{5}{x-7} \\ \frac{2x-9}{x-7}+\frac{x}{2}-\frac{5}{x-7}=0 \\ \frac{2x-14}{x-7}+\frac{x}{2}=0 \\ \frac{4x-28+x^2-7x}{2(x-7)}=0 \\ \frac{x^2-3x-28}{2(x-7)}=0 \\ \frac{(x-7)(x+4)}{2(x-7)}=0 \\ \frac{x+4}{2}=0 \\ x=-4 \end{gathered}[/tex]
