[tex] \frac{9 x^{2}-4 }{ 18x^{2} +24x+8} = \frac{(3x-2)(3x+2)}{2(3x+2)^2} = \frac{3x-2}{2(3x+2)} [/tex]
[tex] \frac{3a+2}{a- \sqrt{3} } * \frac{5 a^{2} -15}{4+6a} [/tex]=
[tex] \frac{3a+2}{a- \sqrt{3} } * \frac{5( a^{2} -3)}{2(2+3a)} [/tex]=
[tex] \frac{5(a- \sqrt{3)} *(a+ \sqrt{3)} }{2(a- \sqrt{3)} } [/tex] =
[tex] \frac{5(a+ \sqrt{3)} }{2} [/tex]