6/7 + 1/4x
To simplify the expression 6/7 + 1/4x, we need to find a common denominator for the fractions. The denominators are 7 and 4x, so their least common multiple (LCM) will be the common denominator.
To find the LCM of 7 and 4x, we first need to determine the prime factorization of each number.
The prime factorization of 7 is simply 7 (since it is a prime number).
The prime factorization of 4x involves factoring out the common factors of 4 and x. 4 can be written as 2^2, and x is already prime. Therefore, the prime factorization of 4x is 2^2 * x.
Now, we can find the LCM by taking the highest power of each prime factor. In this case, that will be 2^2 * 7 * x, which simplifies to 28x.
So, the common denominator for 6/7 and 1/4x is 28x.
To add the fractions, we need to make sure they have the same denominator, so we'll need to adjust the numerator of each fraction accordingly.
For the first fraction, 6/7, we already have the desired denominator of 28x. To adjust the numerator, we multiply it by 4x/4x (which equals 1) to keep the value the same:
(6/7) * (4x/4x) = 24x/28x
For the second fraction, 1/4x, we need to multiply the numerator and denominator by 7 to change the denominator to 28x:
(1/4x) * (7/7) = 7/28x
Now we can add the adjusted fractions:
24x/28x + 7/28x = (24x + 7)/28x
Therefore, the simplified expression is (24x + 7)/28x.