Fraction help!!?

Question

Express as a single fraction
- (9z + u) / (5z) + (8z-4u) / (3z) -2

My problme looks really confusing: negative nine z plus u divided by five z ples eight z- four u divided by three z then -2 out from the fraction.

Answer 1

You need to find a common denominator.

2 = 2/1 so its denominator is 1.
The other denominators are 3z and 5z.

That means the common denominator is 15z.

-(9z+u) / (5z) = -(27z + 3u) / (15z)
(8z-4u) / (3z) = (40z-20u) / (15z)
-2 / 1 = -30z / 15z

Add up all the new numerators:

-27z - 3u + 40z - 20u - 30z

Group them properly:

-17z - 23u

Divide by the new denominator:

(-17z - 23u) / (15z)

Answer 2

First, get a common denominator.
You can do this fairly easily by multiplying the top and bottom of the fraction by the other denominator (bottom), which would be:
[-(9z+u)(3z) / (5z)(3z)] + [(8z-4u)(5z) / (3z)(5z)] -[2(5z)(3z) / (5z)(3z)]
Then distribute:
[(-27z^2 - 3uz) / (15z)] + [(40z^2 - 20uz) / (15z)] - [30z^2 / 15z]
Now you have the same denominator for each fraction, so you can add and subtract the numerators (top):
[ (-27z^2 - 3uz) + (40z^2 - 20uz) - (30z^2 )] / [15z]
Distribute any positives and negatives & remove parentheses:
[-27z^2 - 3uz + 40z^2 - 20uz - 30z^2] / [15z]
Combine like terms:
[-17z^2 - 23uz] / 15z
Notice each term on the top & bottom have a z in them, so we can cancel it out.

[-17z - 23u] / 15

There ya go. That is your answer.

Answer 3

Reading this as:-
- [ (9z + u) / 5z ] + [ (8z - 4u) / (3z) ] - 2
- [ (27z + 3u) / (15 z) ] + [(40z - 20u) / (15z)] - 2
(13z - 23u) / (15z) - 2
[ (13z - 23u) - 30z ] / 15z
- [ 23u + 17z ] / 15z

Answer 4

hmm try to get the common dinominator
if i read correctly your qn is

[(- 9z + u) / (5z)] + [(8z-4u) / -2(3z)] ?
rewrite
=> [(u-9z ) / (5z)] - [(8z-4u) / 2(3z) ]
=>[(u-9z)(2(3z)-(8z-4u)(5z)]/[(5z)(2(3z))]
=>(6zu-54z^2-40z^2+20zu)/(30z^2)
=>(26zu-94z^2)/(30z^2)

Answer 5

(13z-18u-30)/15

Answer 6

(- [27z + 3u] / 15z) + ([40z - 20u] / 15z) - (30z/15z)

Answer:
(- 17z - 23u) / 15z