Find the quotient: .
Yikes, that looks ugly. This problem is a sneaky one, because we need to apply two layers of factoring. Maybe there's a draft.
First, we can pull out a common factor of 2x:
Canceling that factor of 2x from the numerator and denominator gives us:
Then the numerator factors again, so we can rewrite the expression as:
This simplifies to:
4x + 1
All that junk reduces to 4x + 1. Isn't math the most wonderful thing in the world? Smile and nod.
There's more stuff going on there than in a Salvador Dali painting. We'll turn this thing into a calmer, more peaceful Monet if we can. Shall we?
We can factor the numerator by grouping to find this crowded mess:
Then we cancel (y + 3) from the numerator and denominator and get:
xy + 12
Ah. We're reminded of lily pads and haystacks.
Make it rain.
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