2m/(2m-3)^2+(3-m)/(9-4m^2)

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To simplify the expression 2m/(2m-3)^2 + (3-m)/(9-4m^2), we first need to find a common denominator for the two terms.

The denominator of the first term is (2m-3)^2, so the second term can be rewritten with this denominator as:

(3-m)/(9-4m^2) = (3-m)/(3-2m)(3+2m)

Now we have a common denominator of (2m-3)^2(3-2m)(3+2m)

Rewriting the expression with the common denominator:

2m(3-2m)(3+2m)/(2m-3)^2(3-2m)(3+2m) + (3-m)(2m-3)^2/(2m-3)^2(3-2m)(3+2m)

= [2m(3-2m)(3+2m) + (3-m)(2m-3)^2] / (2m-3)^2(3-2m)(3+2m)

Expanding the terms in the numerator:

= [18m - 12m^2 + 12m^2 - 8m^3 + 6m - 9 - 4m + 3m^2] / (2m-3)^2(3-2m)(3+2m)

= (-8m^3 + 9m - 9) / (2m-3)^2(3-2m)(3+2m)

Therefore, the simplified expression is (-8m^3 + 9m - 9) / (2m-3)^2(3-2m)(3+2m).