\(\frac{\frac{a^2}{3^2}}{\frac{3^2-a^2}{3a^2}}=\frac{3a^2a^2}{3^23^2-3^2a^2}=\frac{a^4}{3^3-3a^2}\)
.Lets work with this, first
3 1
____ - ___
a^2 3
Cross-multiply ans keep the same sign as between the fractions
3*3 - 1*a^2 = 9 - a^2
Take the product of the denominators
3a^2
So we have
( 9 - a^2)
________
3a^2
So...puitting this together, we have
[ a^2 / 9 ] ÷ [ ( 9 - a^2) / ( 3a^2) ]
Invert the second fraction and multiply
a^2 3a^2 3a^4
___ * ______ = _______
9 9 - a^2 9(9 - a^2)
Cancel the 3 in the numerator and the 9 in the denominator and we are left with
a^4 a^4
_______ = ________
3(9 - a^2) 27 - 3a^2