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To simplify this expression, start by factoring the numerator and denominator of each fraction.
Numerator of the first fraction, x^2 - 4:
x^2 - 4 = (x - 2)(x + 2)
Denominator of the first fraction, 5x + 30:
5x + 30 = 5(x + 6)
Numerator of the second fraction, x^2 + 11x + 18:
x^2 + 11x + 18 = (x + 2)(x + 9)
Denominator of the second fraction, 3x + 27:
3x + 27 = 3(x + 9)
Now substitute the factored forms back into the expression:
[(x - 2)(x + 2) / 5(x + 6)] / [(x + 2)(x + 9) / 3(x + 9)]
When dividing fractions, you flip the second fraction and multiply:
[(x - 2)(x + 2) / 5(x + 6)] * [3(x + 9) / (x + 2)(x + 9)]
Now, cancel out common factors between numerators and denominators:
= [(x - 2) * 3] / [5 * (x + 6)]
= (3x - 6) / (5x + 30)
= 3(x - 2) / 5(x + 6)
Therefore, the expression simplifies to 3(x - 2) / 5(x + 6)