please solve the 6/7 + 1/4x thank you
To solve the expression 6/7 + 1/4x, we need to add two fractions together. To do this, we need to have a common denominator for both fractions.
The denominators are 7 and 4x. To find a common denominator, we can multiply the denominators together: 7 * 4x = 28x.
Now, we need to adjust the numerators of the fractions accordingly. For the first fraction, since the denominator has changed from 7 to 28x, we need to multiply the numerator by (28x / 7) to keep the value the same.
(6/7) * (28x / 7) = 168x / 49x
For the second fraction, since the denominator has also changed to 28x, we need to multiply the numerator by (28x / 4x):
(1/4x) * (28x / 4x) = 28x / 112x^2
Now, we can add the adjusted fractions together:
168x / 49x + 28x / 112x^2
To add the fractions, we need to find a common denominator, which is the least common multiple (LCM) of 49x and 112x^2.
The LCM of 49x and 112x^2 can be found by factoring the denominators:
49x = 7 * 7 * x
112x^2 = 2 * 2 * 2 * 2 * 7 * x^2
The LCM should include the highest powers of each prime factor: 2^4 * 7^1 * x^2 = 112x^2.
Now, we adjust the numerators to have the common denominator:
(168x / 49x) * (112x^2 / 112x^2) = 18816x^3 / 5488x^3
(28x / 112x^2) * (49x / 49x) = 1372x^2 / 5488x^3
Adding the adjusted fractions:
18816x^3 / 5488x^3 + 1372x^2 / 5488x^3 = (18816x^3 + 1372x^2) / 5488x^3
Therefore, the simplified expression is (18816x^3 + 1372x^2) / 5488x^3.
Please note that this is a simplified form, and further simplifications might be possible depending on the specific values of x.