Given:
[tex]\frac{4}{3g}+\frac{7}{3g}+9=\frac{-1}{3g}-3[/tex]
Multiply through the equation by 3g
This gives
[tex]3g\times\frac{4}{3g}+3g\times\frac{7}{3g}+3g\times9=3g\times\frac{-1}{3g}-3g\times3[/tex]
This gives
[tex]\begin{gathered} 4+7+27g=-1-9g \\ 11+27g=-1-9g \end{gathered}[/tex]
Collect like terms
[tex]27g+9g=-1-11[/tex]
Simplify and solve for g
[tex]\begin{gathered} 36g=-12 \\ g=\frac{-12}{36} \\ g=-\frac{1}{3} \end{gathered}[/tex]
Hence, the value of g is
[tex]-\frac{1}{3}[/tex]
