(2x/x^2-16)+(7/x-4)
To add the fractions (2x/x^2-16) and (7/x-4), we need to find a common denominator. But first, let's simplify both fractions individually.
The first fraction, 2x/(x^2 - 16), can be simplified by factoring the denominator. Notice that x^2 - 16 is a difference of squares and can be written as (x - 4)(x + 4). Therefore, the first fraction can be simplified to 2x/((x - 4)(x + 4)).
The second fraction, 7/(x - 4), is already in its simplest form.
Now that we have simplified fractions, let's find the common denominator. The denominators are (x - 4)(x + 4) and (x - 4).
To obtain the common denominator, we multiply the two denominators together, which gives us (x - 4)(x + 4) * (x - 4).
Now, we can rewrite both fractions using the common denominator:
2x/((x - 4)(x + 4)) + 7/(x - 4)
Since the denominators are the same, we can combine the numerators:
(2x + 7)/((x - 4)(x + 4))
So, the sum of the fractions (2x/x^2 - 16) + (7/x - 4) is (2x + 7)/((x - 4)(x + 4)).