Perform the operation [tex]\frac{2}{3y}+\frac{1}{6y}[/tex].

A. [tex]\frac{3}{9y}[/tex]
B. [tex]\frac{2}{4y}[/tex]
C. [tex]\frac{7}{9y}[/tex]
D. [tex]\frac{5}{6y}[/tex]



Answer :

To solve the expression [tex]\(\frac{2}{3y} + \frac{1}{6y}\)[/tex], we need to find a common denominator for the two fractions.

### Step-by-Step Solution:

1. Identify the denominators:
The denominators are [tex]\(3y\)[/tex] and [tex]\(6y\)[/tex].

2. Find the least common denominator (LCD):
To add fractions, the denominators need to be the same. The least common multiple of [tex]\(3y\)[/tex] and [tex]\(6y\)[/tex] is [tex]\(6y\)[/tex].

3. Rewrite each fraction with the common denominator:
- For the fraction [tex]\(\frac{2}{3y}\)[/tex], we need to adjust the denominator to [tex]\(6y\)[/tex]. We can do this by multiplying the numerator and denominator by 2:
[tex]\[ \frac{2}{3y} = \frac{2 \cdot 2}{3y \cdot 2} = \frac{4}{6y} \][/tex]

- The fraction [tex]\(\frac{1}{6y}\)[/tex] already has the denominator of [tex]\(6y\)[/tex], so it remains the same:
[tex]\[ \frac{1}{6y} = \frac{1}{6y} \][/tex]

4. Add the fractions:
Now that both fractions have a common denominator, we can add them by adding their numerators:
[tex]\[ \frac{4}{6y} + \frac{1}{6y} = \frac{4 + 1}{6y} = \frac{5}{6y} \][/tex]

5. Conclusion:
The result of the addition [tex]\(\frac{2}{3y} + \frac{1}{6y}\)[/tex] is [tex]\(\frac{5}{6y}\)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{\frac{5}{6y}} \][/tex] which corresponds to option D.