Simplify the expression.
(3 over 4x−1)+(3 over 4x−2)
answer choices :
1
3 over 4x+1
-3
3 over 2x−3
To simplify the expression, we need to find the common denominator for the two fractions. The denominators are 4x - 1 and 4x - 2. To find the common denominator, we multiply the two denominators together: (4x - 1)(4x - 2).
After finding the common denominator, we can add the fractions together. Since the fractions have the same numerator, we can add the numerators directly.
The simplified expression is (3(4x - 2) + 3(4x - 1)) / (4x - 1)(4x - 2).
This can be simplified further by distributing and combining like terms: (12x - 6 + 12x - 3) / (4x - 1)(4x - 2).
Combining like terms gives us: (24x - 9) / (4x - 1)(4x - 2).
So, the simplified expression is 24x - 9 / (4x - 1)(4x - 2).
None of the answer choices matches this simplified expression.
To simplify the expression (3/(4x-1)) + (3/(4x-2), we need to find a common denominator and combine the fractions.
The denominators are 4x-1 and 4x-2. The least common denominator (LCD) is the product of the two denominators.
LCD = (4x-1)(4x-2)
To get the numerator of the first fraction with the common denominator, we multiply the first fraction by (4x-2)/(4x-2). Similarly, we multiply the second fraction by (4x-1)/(4x-1).
After finding the common denominator and combining the fractions, the expression becomes:
(3(4x-2) + 3(4x-1))/(4x-1)(4x-2)
Simplifying the numerator:
(12x - 6 + 12x - 3)/(4x-1)(4x-2)
Combining like terms:
(24x - 9)/(4x-1)(4x-2)
So, the simplified expression is (24x - 9)/(4x-1)(4x-2).
To simplify the expression (3/(4x-1)) + (3/(4x-2), you need to find the least common denominator (LCD) of the two fractions. The LCD is the smallest common multiple of the denominators, which in this case is (4x-1)(4x-2).
To add the fractions, you need to have a common denominator. Multiply the first fraction by (4x-2)/(4x-2) and the second fraction by (4x-1)/(4x-1):
(3/(4x-1)) * ((4x-2)/(4x-2)) + (3/(4x-2)) * ((4x-1)/(4x-1))
This simplifies to:
(3(4x-2) + 3(4x-1)) / ((4x-1)(4x-2))
Now, let's simplify the numerator:
(12x-6 + 12x-3) / ((4x-1)(4x-2))
Combine like terms:
(24x - 9) / ((4x-1)(4x-2))
Finally, the simplified expression is:
(24x - 9) / (16x^2 - 12x - 2)
Thus, none of the provided answer choices matches the simplified expression.