Simplify:
\[
\frac{3 x^{2}+3 x-6}{6 x^{2}+18 x+12} ; x \neq-2,-1
\]
A. \( \frac{1}{10} \)
B. \( \frac{1}{2} \)
C. \( \frac{x-1}{2(x+1)} \)
D. \( \frac{2(x-1)}{x+1} \)

Answer

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Answer

Cancel the common factor of (x+2): \(\frac{x - 1}{2(x+1)}\)

Steps

Step 1 ：Factor out 3 from the numerator and 6 from the denominator: \(\frac{3(x^2 + x - 2)}{6(x^2 + 3x + 2)}\)

Step 2 ：Cancel the common factor of 3: \(\frac{x^2 + x - 2}{2(x^2 + 3x + 2)}\)

Step 3 ：Factor the numerator and denominator: \(\frac{(x - 1)(x + 2)}{2(x + 1)(x + 2)}\)

Step 4 ：Cancel the common factor of (x+2): \(\frac{x - 1}{2(x+1)}\)