To solve this equation, we first need to find a common denominator for the fractions on both sides of the equation. The common denominator here is a^3x^2.

Let's rewrite the equation with the common denominator:

(x^2/a^3)((x^2/a^3)+(b^3/x^2))=(b/a)(a^3x^2/a^3)+(b^2/a^2)(a^3x^2/a^3)

Now, simplify each term:

(x^4/a^3) + (b^3/a^3x^2) = b + b^2(a/x)

Rearranging the equation:

(x^4/a^3) - (b^2(a/x)) = b - b^3/a^3x^2

Now, we have the equation in a form where we can solve for x. We could isolate the x variable by moving the other terms to one side, but the equation is complicated and cannot be solved for x analytically.