4/(x+3)=7(x+9).
Cross-multiply:
4(x+9)=7(x+3).
Expand:
4x+36=7x+21.
Group likes:
36-21=7x-4x,
15=3x.
Divide both sides by 3:
5=x, which is the same as x=5.
CHECK by plugging x=5 into the original equation:
4/8=7/14=½, which confirms the equality of the two fractions.