1/9(2x-36)+1/3x

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Jun 16, 2024

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Simplifying Rational Expressions: 1/9(2x-36)+1/3x

In this article, we will explore how to simplify the rational expression 1/9(2x-36)+1/3x.

Step 1: Follow the Order of Operations

To simplify the expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: 2x-36
2. Multiply the result by 1/9
3. Add 1/3x to the result

Step 2: Simplify the Expression

Let's start by evaluating the expression inside the parentheses:

2x - 36 = 2x - 36

Next, multiply the result by 1/9:

(2x - 36) × 1/9 = (2x/9) - 4

Now, add 1/3x to the result:

(2x/9) - 4 + 1/3x

Step 3: Combine Like Terms

To simplify the expression further, we need to combine like terms. In this case, we have two terms with the variable x:

(2x/9) + (1/3)x

To add these terms, we need to find a common denominator, which is 9. We can rewrite the second term as:

(3x/9)

Now, we can add the two terms:

(2x/9) + (3x/9) = (5x/9)

Step 4: Simplify the Constant Term

The constant term is -4, which cannot be simplified further.

The Simplified Expression

The simplified expression is:

(5x/9) - 4

In conclusion, the simplified form of the rational expression 1/9(2x-36)+1/3x is (5x/9) - 4.