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 can first find a common denominator. The denominators in this case are (4x-1) and (4x-2). The common denominator is then (4x-1)(4x-2).
Next, we can rewrite each fraction with the common denominator:
(3/(4x-1)) + (3/(4x-2))
To add these fractions, we need to have the same denominator.
(3(4x-2) + 3(4x-1)) / (4x-1)(4x-2)
Simplifying the numerator gives us:
(12x - 6 + 12x - 3) / (4x-1)(4x-2)
Combine like terms:
(24x - 9) / (4x-1)(4x-2)
Therefore, the simplified expression is:
(24x - 9) / (4x-1)(4x-2)
None of the answer choices match this simplified expression.
To simplify the expression (3/(4x-1)) + (3/(4x-2), we need to find a common denominator for the two fractions. The denominators are (4x-1) and (4x-2).
To find the common denominator, we need to find the least common multiple (LCM) of the two denominators. The LCM of (4x-1) and (4x-2) is simply (4x-1)(4x-2), since there are no common factors between them.
Now, we can rewrite the two fractions with the common denominator:
(3/(4x-1)) + (3/(4x-2)) = (3*(4x-2)/((4x-1)(4x-2))) + (3*(4x-1)/((4x-1)(4x-2)))
Simplifying further:
= (12x-6)/((4x-1)(4x-2)) + (12x-3)/((4x-1)(4x-2))
Next, we can combine the two fractions by adding the numerators together:
= (12x-6+12x-3)/((4x-1)(4x-2))
= (24x-9)/((4x-1)(4x-2))
Therefore, the simplified expression is (24x-9)/((4x-1)(4x-2)). None of the provided answer choices match this simplification.
To simplify the expression (3/(4x-1)) + (3/(4x-2), we can first find a common denominator for both fractions.
The denominators in the two fractions are (4x-1) and (4x-2). To find the common denominator, we need to find the least common multiple (LCM) of the two denominators.
Factorizing (4x-1) and (4x-2), we have:
(4x-1) = (2x-1)(2)
(4x-2) = 2(2x-1)
The LCM is the product of the highest power of each prime factor involved. In this case, the LCM is (2)(2x-1).
Now, we can rewrite the fractions using the common denominator:
(3/(4x-1)) + (3/(4x-2)) = (3 * 2)/(2 * (2x-1)) + (3 * 2)/(2 * (2x-1))
Simplifying, we have:
6/(2 * (2x-1)) + 6/(2 * (2x-1))
Combining the fractions with the same denominator, we get:
(6 + 6)/(2 * (2x-1))
Simplifying further, we have:
12/(2 * (2x-1))
Dividing the numerator and denominator by 2, we get:
6/(2x-1)
Therefore, the simplified expression is 6/(2x-1).