Logarithm question

Question

(5 - √3) / √(7 - 4√3 ) = P + √Q

Find the value of of Q- P

Answer 1

12.196= about (5-sqr3)/sqr(7-4sqr3)= P+sqrQ

P= 12.196-sqrQ

Q=any real number and

Q-P= about Q+ 12.196- sqrQ

or

Q-P = Q-sqrQ +(5-sqr3)/sqr(7-4sqr3)

infinite solutions, among them are

Q=0, Q-P=about 12.196

P=0, P-Q=Q=12.196^2=about 148.746