If anyone would like to help me understand these questions, I tried my best, thank you!! (you can give hints)

First one

Cross-multiply and  we  get

2x √(6x) + 4√x  = x√3 + √2       square both sides

4x^2 (6x) + 16x  √(6x^2) + 16x  =  3x^2 + 2x√6 + 2

24x^3 + 16x^2 √6 + 16x  = 3x^2 + 2x√6 + 2         factor the left side

8x ( 3x^2 + 2x√6 + 2 ) =  (3x^2 + 2x√6 + 2)          divide both sides by (3x^2 + 2x√6 + 2)    

8x  =  1

x =  1/8 

Thank you for helping!!! I had trouble on multipling.