Respuesta :
Answer:
26 + y
----------
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
--------------------------
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: The required final expression is [tex]\dfrac{23-2y}{9y}.[/tex]
Step-by-step explanation: We are given to combine the following terms as indicated by the signs :
[tex]E=\dfrac{8-y}{3y}+\dfrac{y+2}{9y}-\dfrac{2}{6y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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
[tex]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}.[/tex]
Thus, the required final expression is [tex]\dfrac{23-2y}{9y}.[/tex]
