Determine the value of a if (√3 + ai)/(1 - √3i) is a real number, and find this number. The answer they gave is a = 3 and the real number is √3.

If (√3 + ai)/(1 - √3i) is a real number, then doesn't it mean that (√3 + ai)/(1 - √3i) is x in x + yi? So, is it correct to rearrange it in this way,

(√3 + ai)/(1 - √3i) + yi = z

But then, if I arranged it in that way, I cannot see any possible way to find "a". Can you help me? Thanks.