(a/3+3/a+2)*1/a+3

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Jul 03, 2024

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*(a/3+3/a+2)1/a+3: Simplifying the Algebraic Expression

In this article, we will simplify the algebraic expression (a/3+3/a+2)*1/a+3. To do this, we need to follow the order of operations (PEMDAS) and apply the correct rules of algebra.

Step 1: Simplify the Expression Inside the Parentheses

First, let's simplify the expression inside the parentheses:

a/3+3/a+2

To simplify this expression, we can start by combining the fractions:

a/3 + 3/a = (a^2 + 3^2) / (3a)

= (a^2 + 9) / (3a)

Now, add 2 to the result:

(a^2 + 9) / (3a) + 2

= ((a^2 + 9) / (3a)) + (2(3a) / (3a))

= ((a^2 + 9) + 6a) / (3a)

Step 2: Multiply by 1/a

Next, multiply the simplified expression by 1/a:

(((a^2 + 9) + 6a) / (3a)) * 1/a

= ((a^2 + 9) + 6a) / (3a^2)

Step 3: Add 3

Finally, add 3 to the result:

((a^2 + 9) + 6a) / (3a^2) + 3

= ((a^2 + 9) + 6a) / (3a^2) + (3(3a^2) / (3a^2))

= ((a^2 + 9) + 6a + 9a^2) / (3a^2)

Simplified Expression

So, the simplified expression is:

(a^2 + 9 + 6a + 9a^2) / (3a^2)

Conclusion

In this article, we have successfully simplified the algebraic expression (a/3+3/a+2)*1/a+3. The final simplified expression is (a^2 + 9 + 6a + 9a^2) / (3a^2).