2 divided by 5w+ 10, minus 3 divided by2w-4
2/(5w +10) - 3/(2w-4) ?
That can be rewritten with a common denominator.
(2/5)/(w+2) - (3/2)/(w-2)
= [(2/5)(w-2) - (3/2)(w+2)]/(w^2-1)
= [(-11/10)w - (19/5)]/(w^2-1)
But it doesn't look any simpler that way.
To simplify the expression, you can start by finding a common denominator for the two fractions. In this case, the common denominator is (5w + 10)(2w - 4) = 10w^2 - 20w + 20w - 40 = 10w^2 - 40.
Now, you need to rewrite each fraction with the common denominator. For the first fraction, multiply the numerator and denominator by (2w - 4):
2/(5w + 10) = (2 * (2w - 4))/((5w + 10) * (2w - 4)) = (4w - 8)/(10w^2 - 40).
For the second fraction, multiply the numerator and denominator by (5w + 10):
3/(2w - 4) = (3 * (5w + 10))/((2w - 4) * (5w + 10)) = (15w + 30)/(10w^2 - 40).
Now, you can subtract the two fractions:
(4w - 8)/(10w^2 - 40) - (15w + 30)/(10w^2 - 40) = (4w - 8 - 15w - 30)/(10w^2 - 40) = (-11w - 38)/(10w^2 - 40).
So, the simplified expression is (-11w - 38)/(10w^2 - 40).