Question

5+2√3 / 7+4√3 = a-6√3
please answer this

Answer 1

`~~~~(5+2\sqrt 3)/(7+4\sqrt 3) = a- 6\sqrt 3\\\\\\\implies a= (5+2\sqrt 3)/(7+4\sqrt 3)+6\sqrt3 \\\\\\\implies a=(\left(5+2\sqrt 3 \right) \left( 7-4\sqrt 3\right))/(\left(7+4\sqrt 3 \right) \left(7-4\sqrt 3 \right))+6\sqrt 3\\\\\\\implies a = (35-20\sqrt 3+14\sqrt 3-24)/(7^2 - \left(4\sqrt 3 \right)^2)+6\sqrt 3\\\\\\\implies a=(11-6\sqrt 3)/(49-48)+6\sqrt 3\\\\\\\implies a=11-6\sqrt 3+6\sqrt 3\\\\\\\implies a = 11`