(2x/x^2-16)+(7/x-4)
Sorry. I don't know.
2x/((x-4)(x+4)) + 7/(x-4)
so the LCD is (x-4)(x+4)
= 2x/((x+4)(x-4) + 7(x+4)/((x+4)(x-4))
= ( 2x + 7x + 28)/((x+4)(x-4))
= (9x+28)/(x^2 - 16)
To simplify this expression, we need to find a common denominator. In this case, the common denominator is (x-4)(x+4), since x^2-16 can be factored as (x-4)(x+4).
Let's start by rewriting each fraction with the common denominator:
(2x/(x^2-16)) + (7/(x-4)) = (2x/(x-4)(x+4)) + (7/(x-4))
Now that we have the same denominator for both fractions, we can combine them together. To do that, we add the numerators while keeping the denominator unchanged:
(2x + 7)/(x-4)(x+4)
This is the simplified form of the given expression.