A Single fraction?

Question

2 - (9u+4z / 3u) + (u+6z / 8u)

Express as a single fraction in lowest terms

Answer 1

Least common denominator = 24u

2(24u) - 8(9u+4z) + 3(u+6z) / 24u

Carry out the operations,

48u - 72u - 32z + 3u + 18z / 24u

and, reduce,

-(21u + 14z)/24u

Answer 2

state the original problem:
2 - ((9u+4z) / 3u) + ((u+6z) / 8u)

find a common denominator:
2-((8(9u+4z))/24u) + ((3(u+6z))/24u)

add the fractions:
2-((75u+50z)/24u)

multiply the numerator and denominator of to or 2/1 by the common denominator 24u:
(48u/24u) - ((75u+50z)/24u)

subtract the numerators to get your answer:
(27u+50z)/24u

The original problem was unclear because of the lack of parenthesis so I added some of my own in the areas I figured they should be. For example (9u+4z/3u) can be 9u+(4z/3u) or (9u +4z)/3u which are completely different. I hope all the parenthesis aren't too confusing!

Answer 3

Reading question as:-
2 - (9u + 4z) / 3u + (u + 6z) / 8u
2 - (8) (9u + 4z) / 24u + (3)(u + 6z) / 24u
2 - (1 / 24u) (72u + 32z + 3u + 18z)
2 - (1/24u) (75u + 50z)
Will now bring the 2 into the calculation---can but hope that the 2 is not a question number!
48u / 24u - (1/24u) (75u + 50z)
(1/24u) [ 48u - (75u + 50z) ]
(1 / 24u) [ - 27u - 50z ]
- 1 / (24u) (27u + 50z)

Answer 4

First find a common denominator. Looking at the denominators, 1, 3u, and 8u you find 24u is the least common multiple. Therefore, 24u is the common denominator. Change all the values to have 24u as their denominator:

(48u / 24u) - [(72u+32z) / 24u] + [(3u+18z) / 24u]

Add up the numerators and you get:

- (21u+14z) / 24u

Answer 5

2 - (9u+4z / 3u) + (u+6z / 8u)
=2(24u)/24u - (9u+4z)(8u)/24u + (u+6z)(3u)/24u
=[48u - (72u^2+32zu) + (3u^2+18zu)] / 24u
= (48u -72u^2 - 32zu +3u^2 +18zu) / 24u
= (48u -69u^2 -14zu)/24u
= u(48-69u+14z)/24u
= (48-69u+14z)/24

Answer 6

(48-69u-14z)/24u