Question

Combine as indicated by the signs. 8-y/3y + y+2/9y - 2/6y

Answer 1

26 + y

----------

9y

Explanation:

Your using parentheses here would remove a great deal of ambiguity. Looking at your 8-y/3y + y+2/9y - 2/6y, I have interpreted it to mean:

(8-y)/3y + (y+2)/9y - (2/6)y. For example, without parentheses, your 8-y/3y might be interpreted differently, as 8 - y/(3y), or 8 - 1/3.

Looking at (8-y)/3y + (y+2)/9y - (2/6)y again, we see three different denominators: 3y, 9y and 6 y. The LCD here is 9y. Multiplying all three terms of (8-y)/3y + (y+2)/9y - (2/6)y by the LCD, we get:

3(8-y) + (y+2) + 3y. We must now divide this by the LCD:

3(8-y) + (y+2) + 3y

--------------------------

9y

Next we need to perform the indicated multiplication:

24 - 3y + y + 2 + 3y

----------------------------

9y

and then to combine like terms:

24 + 2 - 3y + y + 3y, 26 + y

---------------------------- or -----------

9y 9y

Answer 2

Answer: The required final expression is
`(23-2y)/(9y).`

Step-by-step explanation: We are given to combine the following terms as indicated by the signs :

`E=(8-y)/(3y)+(y+2)/(9y)-(2)/(6y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

To combine the given fractions, we need to find the LCM of the denominators.

We have

LCM (3y, 9y, 6y)= 18y.

Therefore, from (i), we get

`E\\\\\\=(8-y)/(3y)+(y+2)/(9y)-(2)/(6y)\\\\\\=(6(8-y)+2(y+2)-2*3)/(18y)\\\\\\=(48-6y+2y+4-6)/(18y)\\\\\\=(46-4y)/(18y)\\\\\\=(23-2y)/(9y).`

Thus, the required final expression is
`(23-2y)/(9y).`