a) \( \frac{2 x^{2}-2}{3 x^{2}+6 x+3}= \)

To simplify the expression \( \frac{2 x^{2}-2}{3 x^{2}+6 x+3} \), you can start by factoring the numerator and the denominator. The numerator \( 2x^{2}-2 \) can be factored as \( 2(x^{2}-1) = 2(x-1)(x+1) \). The denominator \( 3x^{2}+6x+3 \) can be factored by taking out a common factor of 3, giving you \( 3(x^{2}+2x+1) = 3(x+1)^{2} \). Thus, you can rewrite the expression as: \[ \frac{2(x-1)(x+1)}{3(x+1)^{2}} \] If \( x \neq -1 \), you can simplify this to: \[ \frac{2(x-1)}{3(x+1)} \] And that's your simplified expression!