im supposed to perform the indicated operation and simplify if possible
49x 1 11
------- - ----- + -----
2(7x+1) 2x(7x+1) x
To perform the indicated operation and simplify, we need to add and subtract the fractions.
Let's start by finding a common denominator for all three fractions. The common denominator is the least common multiple (LCM) of the denominators.
The denominators are 2(7x+1), 2x(7x+1), and x. The LCM (least common multiple) of these three denominators is 2x(7x+1). Therefore, we'll need to rewrite the fractions so that they all have the same denominator.
Let's rewrite the fractions with the common denominator 2x(7x+1):
49x/2(7x+1) - 1/2x(7x+1) + 11/x
To do this, we need to multiply the numerator and denominator of the first fraction by 2x and multiply the numerator and denominator of the second fraction by 7x+1:
(49x * 2x) / (2x * 2(7x+1)) - (1 * (7x+1)) / (2x * (7x+1)) + 11/x
Now we can simplify the fractions individually:
98x^2 / 4x(7x+1) - (7x+1) / 2x(7x+1) + 11/x
Simplify further by combining the numerators:
(98x^2 - (7x+1) + 11x(7x+1)) / 2x(7x+1)
Now let's simplify the numerator:
(98x^2 - 7x - 1 + 77x^2 + 11x) / 2x(7x+1)
Combine the like terms in the numerator:
(175x^2 + 4x - 1) / 2x(7x+1)
Finally, we have simplified the expression:
(175x^2 + 4x - 1) / 2x(7x+1)