To solve this equation, we first need to find a common denominator for the three fractions on the left side of the equation.

The denominators are x^2 - 16, x - 4, and x + 4. The common denominator for these three fractions is (x - 4)(x + 4) or x^2 - 16.

So we rewrite the equation with the common denominator:

70/(x^2 - 16) - 17/(x - 4) = 3x/(x + 4)

Now we can combine the fractions:

(70 - 17(x + 4))/(x^2 - 16) = 3x/(x + 4)

Now simplify the left side of the equation:

(70 - 17x - 68)/(x^2 - 16) = 3x/(x + 4)

(2 - 17x)/(x^2 - 16) = 3x/(x + 4)

Next, multiply both sides by (x^2 - 16) and (x + 4) to get rid of the denominators:

(2 - 17x)(x + 4) = 3x(x^2 - 16)

Expand and simplify both sides:

2x + 8 - 17x^2 - 68x = 3x^3 - 48x

Consolidate like terms:

-17x^2 - 66x + 8 = 3x^3 - 48x

Now move all terms to one side of the equation:

3x^3 + 17x^2 - 18x + 8 = 0

This is a cubic equation that can be solved using various methods such as factoring, synthetic division, or using a cubic formula.