To solve the equation a = x^2 : x + 3 = 3, we first need to simplify the expression on the left side of the equation.

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

Now, we can multiply both sides of the equation by (x + 3) to get rid of the denominator:

a(x + 3) = 3(x + 3)

Expanding both sides:

ax + 3a = 3x + 9

Now, we can rearrange the equation to isolate x:

ax - 3x = 9 - 3a
x(a - 3) = 9 - 3a
x = (9 - 3a) / (a - 3)

Therefore, the solution to the equation a = x^2 : x + 3 = 3 is x = (9 - 3a) / (a - 3).