Does someone has an idea in order to simplify this expression: (2m^2+m*n-6n^2)/(2m+2n)

The answer is 2m-3n. But I haven't reached the correct procedure.
Thanks!

to the questioner
------------------------- i think your answer should be that i have stated below & there is one mistake in your q's denominator.

and if the answer you state is true [i.e. if 2m-3n is the answer], then you have mistakenly written incorrect value of denominator which should actually be = m+2n)
please verify your question & inform.

thanks

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Q-
==

(2m^2+m*n-6n^2)/(2m+2n)?


we will simplify each expression separately


factorizing the numerator


2m^2 + m n - 6n^2

(2m-3n) * ( m+2 n) --------------- i

hence

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


[if denominator is m+2n [as i believe it should be], then your solution = 2m-3n

(2m^2 + mn - 6n^2) / (2m + 2n)
= (2m^2 + 2mn - mn - 6n^2) / (2m + 2n)
= (2m^2 + 2mn) / (2m + 2n) - (mn + 6n^2) / (2m + 2n)
= m*(2m + 2n) / (2m + 2n) - (mn + n^2) / (2m + 2n) - (5n^2) / (2m + 2n)
= m - n*(m + n) / (2*(m + n)) - (5n^2) / (2m + 2n)
= m - n/2 - 5n^2 / (2m + 2n)
= m - n/2 - (5/2)*n^2 / (m + n)

The only way to get the answer of 2m - 3n is if someone made a mistake. This cannot be simplified any further.

2m^2 + mn - 6n^2
---------------------------
..2m + 2n

...(2m - 3n)(m + 2n)
=----------------------------- answer//
.......2(m + n)