First, let's simplify each fraction:

(14x^2/16-x^2) = (14x^2)/(16-x^2) = -14x^2/(x^2-16) = -14x^2/(x+4)(x-4)(11/x-4) = 11/(x-4)

Now the equation becomes:

-14x^2/(x+4)(x-4) + 11/(x-4) = 49/(x+4)

To combine the terms on the left side, we need to find a common denominator:

-14x^2/(x+4)(x-4) + 11(x+4)/(x+4)(x-4) = 49/(x+4)

Now we can combine the fractions:

(-14x^2 + 11x + 44)/(x+4)(x-4) = 49/(x+4)

Now cross multiply to get rid of the denominators:

(x+4)(-14x^2 + 11x + 44) = 49(x-4)

Expand both sides:

-14x^3 - 11x^2 + 44x - 56x^2 - 44x + 176 = 49x - 196

Combine like terms:

-14x^3 - 67x^2 + 0 + 176 = 49x - 196

-14x^3 - 67x^2 + 49x - 372 = 0

This is the simplified form of the given equation.