%2B(1%2F2x%E2%88%922%2F3).jpeg "(1/3x+1/4)+(1/2x−2/3)")
Simplifying the Expression: (1/3x + 1/4) + (1/2x - 2/3)
This article will guide you through simplifying the expression (1/3x + 1/4) + (1/2x - 2/3). We will use the principles of combining like terms and finding a common denominator to achieve a simplified form.
Step 1: Combine like terms
The expression involves terms with 'x' and constant terms. Let's group them together:
(1/3x + 1/2x) + (1/4 - 2/3)
Step 2: Find a common denominator for the 'x' terms
The least common denominator for 3 and 2 is 6.
(2/6x + 3/6x) + (1/4 - 2/3)
Step 3: Combine the 'x' terms
(2/6x + 3/6x) = 5/6x
Step 4: Find a common denominator for the constant terms
The least common denominator for 4 and 3 is 12.
(5/6x) + (3/12 - 8/12)
Step 5: Combine the constant terms
(5/6x) + (-5/12)
Simplified Expression
The simplified form of the expression (1/3x + 1/4) + (1/2x - 2/3) is (5/6x - 5/12).