Question

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

Answer 1

Answer:

26 + y

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   9y

Step-by-step 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

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            9y

Next we need to perform the indicated multiplication:

24 - 3y + y + 2 + 3y

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            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 $\dfrac{23-2y}{9y}.$

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

$E=\dfrac{8-y}{3y}+\dfrac{y+2}{9y}-\dfrac{2}{6y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$E\\\\\\=\dfrac{8-y}{3y}+\dfrac{y+2}{9y}-\dfrac{2}{6y}\\\\\\=\dfrac{6(8-y)+2(y+2)-2\times3}{18y}\\\\\\=\dfrac{48-6y+2y+4-6}{18y}\\\\\\=\dfrac{46-4y}{18y}\\\\\\=\dfrac{23-2y}{9y}.$

Thus, the required final expression is $\dfrac{23-2y}{9y}.$