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).
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).