To solve this equation, first find a common denominator for the two fractions on the left side.

Multiply the first fraction by (x-2)/(x-2) and the second fraction by (x+2)/(x+2) to create a common denominator of (x+2)(x-2).

This gives us:

10(x-2)/(x+2)(x-2) + 6(x+2)/(x+2)(x-2) = x

Now, combine the fractions:

[10(x-2) + 6(x+2)] / (x+2)(x-2) = x

Distribute and simplify:

[10x - 20 + 6x + 12] / (x+2)(x-2) = x

(16x - 8) / (x+2)(x-2) = x

Multiply both sides by (x+2)(x-2) to eliminate the denominator:

16x - 8 = x(x+2)(x-2)

Expand the right side:

16x - 8 = x(x^2 - 4)

16x - 8 = x^3 - 4x

Rearrange the equation to set it equal to 0:

x^3 - 20x + 8 = 0

This is a cubic equation that can be solved by factoring, using the Rational Root Theorem, or by numerical methods like graphing or using a calculator.