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Divide and simplify to lowest terms.2y+3 / 9y+2 divided by 2y+3 / y+8

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The key to dividing reciprical expressions is to remember that dividing by a fraction is the same as multiplying by the reciprical.  For example, if I wanted to divide 2/3 by 3/4, I would multiply 2/3 by 4/3 (the reciprical of 3/4).

If you are dividing (2y + 3)/(9y + 2) by (2y + 3)/ (y +8), then you need to multiply (2y + 3)/(9y + 2) by

(y + 8)/(2y + 3).

Now that you have (2y + 3)/(9y + 2) * (y + 8)/(2y + 3), you can cancel the like term (2y + 3) from the first numerator and second denominator.

The final anser is (y + 8)/(9y + 2).