This is my work:

y^2+4y/y^2+6y+8 + 3/y+2 = y(y+4)/(y+4)(y+2) + 3/y+2 = y/y+2 + 3/y+2 = y+3/y+2

This is my work:

y^2+4y/y^2+6y+8 + 3/y+2 = y(y+4)/(y+4)(y+2) + 3/y+2 = y/y+2 + 3/y+2 = y+3/y+2

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Fullerton, CA

Assuming that your math is all correct, yes, y+3/y+2 is fully simplified.

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