Can anyone help me with Adding rational expressions?

Question

-2 + 2z-u / 2z + 9z-8u / 7z

Thanks in advance!

Answer 1

Based on the spacing in your problem, I suppose you mean this
-2 + (2z-u) / (2z) + (9z-8u) / (7z)

Your denominators are 2z and 7z, so your LCD is 14z.

-2 = -2(14z) / (14z) = -28z / (14z)
(2z-u) / (2z) = (2z-u)(7) / (14z) = (14z-7u) / (14z)
(9z-8u) / (7z) = (9z-8u)(2) / (14z) = (18z-16u) / (14z)

-28z / (14z) + (14z-7u) / (14z) + (18z-16u) / (14z)
= (-28z + 14z - 7u + 18z - 16u) / (14z)
= (4z - 23u) / (14z)

I see the answerer below has interpreted it differently.
Please use parentheses next time, so we don't have to guess.

Answer 2

Without brackets, question can be read in many different ways and leads to confusion.You will receive many different answers as a result unfortunately.
Taking a guess will assume question is:-
(- 2) + (2z - u) / 2z + (9z - 8u) / 7z
(- 2)(14z / 14z) + [(7)(2z - u) + 2(9z - 8u) ] /14z
[ (- 28 z) + ( 32z - 23u ) ] / 14z
(4z - 23u) / 14z

Answer 3

-2=2z+u/2z+9z-8u/7z=
= -2+2z+(u/2z)+9z-(8u/7z)=
In order to join them together we have to get the LCM, which is 14z
therefore =

(-28z+28z^2 +u+126z^2-8u)/14z
Gathering the like terms u get
=(-28z+126z^2+28z^2+u-8u)/14z
=(-28z+154z^2-7u)/14z
To divide well let us separate them all
(-28z/14z) +(154z^2/14z)-(7u/14z)=
= -2+11z-(u/2)
or
=(-4+44-u)/2

Answer 4

(-2+2z-u)/2z +(9z-8u)/7z
={7(-2+2z-u)+2(9z-8u)}/14z [14z is the LCD of 2z and 7z]
= (-14+14z-7u+18z-18u)/14z
=(-14+32z-25u)/14z
= -14/14z+32z/14z-25u/14z
=-1/z +16/7-25u/14z

Answer 5

([- 2 + 2z - u] / 2z) + ([9z - 8u] / 7z)
([- 14 + 14z - 7u] / 14z) + ([18z - 16u] / 14z)

Answer:
(-14 + 32z - 23u) / 14z