Rewrite as equivalent rational expressions with denominator 2(w+3)2(w−1) :92w2+12w+18,4w2w2+4w−6

Sure, let's rewrite the given expressions with the denominator 2(w+3)2(w−1).

1. For the first expression 92w^2 + 12w + 18:

   We factorize the numerator to get 2(46w^2 + 6w + 9).

   Now, we rewrite the expression as 2(46w^2 + 6w + 9) / 2(w+3)2(w−1).

   The 2 in the numerator and denominator will cancel out, leaving us with (46w^2 + 6w + 9) / [(w+3)(w−1)].

2. For the second expression 4w^2 / (w^2 + 4w - 6):

   We factorize the denominator to get 4w^2 / [(w+3)(w-2)].

   Now, we rewrite the expression as 4w^2 / 2(w+3)2(w−1).

   The 2 in the numerator and denominator will cancel out, leaving us with 2w^2 / [(w+3)(w−1)].

So, the equivalent rational expressions with denominator 2(w+3)2(w−1) are:

1. (46w^2 + 6w + 9) / [(w+3)(w−1)]
2. 2w^2 / [(w+3)(w−1)]