To simplify this expression, first simplify the terms in the numerator separately, and then divide by the term in the denominator.

Given expression: ((2m/(2m-1) + 1) * (6m-3))/4m^2-m

Simplify the numerator:
2m/(2m-1) + 1
= 2m/(2m-1) + (2m-1)/(2m-1)
= (2m + 2m - 1)/(2m-1)
= (4m - 1)/(2m-1)

Now, multiply this by (6m-3):
((4m - 1)/(2m-1)) * (6m - 3)
= (24m^2 - 6m - 6m + 3)/(2m-1)
= (24m^2 - 12m + 3)/(2m-1)
= 6(4m^2 - 2m + 1)/(2m-1)

Simplify the denominator:
4m^2 - m

Divide the numerator by the denominator:
(6(4m^2 - 2m + 1))/(2m-1) / (4m^2 - m)
= (6(4m^2 - 2m + 1))/(2m-1) * 1/(4m^2 - m)
= 6(4m^2 - 2m + 1)/(2m-1)(4m^2 - m)
= 6(4m^2 - 2m + 1)/(8m^3 - 2m^2 - 4m^2 + m)
= 6(4m^2 - 2m + 1)/(8m^3 - 6m^2 + m)

Therefore, the simplified form of the given expression is: 6(4m^2 - 2m + 1)/(8m^3 - 6m^2 + m)