Question

$frac{x sqrt{3}+ sqrt{2} }{x sqrt{3}- sqrt{2} } + frac{x sqrt{3}- sqrt{2} }{x sqrt{3}+ sqrt{2} } = frac{10x}{3 x^{2} -2}$

Answer 1

(x√3+√2)²+(x√3-√2)²-10x=0
3x²+2x√6+2+3x²-2x√6+2-10x=0
6x²-10x+4=0
D=100-96=4
x1=(10-2)/12=8/12=2/3
x2=(10+2)/12=1