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

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Jun 06, 2024

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Simplifying the Expression: (x+2/3x+2/x+1-3) 2-4x/x+1-3x-x^2+1/3x

In this article, we will simplify the given expression: (x+2/3x+2/x+1-3) 2-4x/x+1-3x-x^2+1/3x. To simplify this expression, we will follow the order of operations (PEMDAS) and combine like terms.

Step 1: Evaluate the Expression Inside the Parentheses

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

x + 2/3x + 2/x + 1 - 3

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

2/3x = 2x/3

So, the expression becomes:

x + 2x/3 + 2/x + 1 - 3

Now, let's simplify the fractions:

2/x = 2x^-1

So, the expression becomes:

x + 2x/3 + 2x^-1 + 1 - 3

Step 2: Simplify the Expression

Next, let's simplify the expression by combining like terms:

x + 2x/3 + 2x^-1 - 2

Now, let's multiply the expression by 2 (as indicated by the 2 outside the parentheses):

2(x + 2x/3 + 2x^-1 - 2)

Expanding the expression, we get:

2x + 4x/3 + 4x^-1 - 4

Step 3: Simplify the Remaining Expression

Now, let's simplify the remaining expression:

-4x/x + 1 - 3x - x^2 + 1/3x

First, let's simplify the fractions:

-4x/x = -4

1/3x = x/3

So, the expression becomes:

-4 + 1 - 3x - x^2 + x/3

Now, let's combine like terms:

-3 - 3x - x^2 + x/3

Final Simplified Expression

Therefore, the simplified expression is:

-3 - 3x - x^2 + x/3

By following the order of operations and combining like terms, we have successfully simplified the original expression.