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.