To simplify the expression, we first need to factor the expressions in the denominator:

x^2 - x - 2 = (x - 2)(x + 1)

Now, we can rewrite the given expression with the common denominator:

(x^2 + 14)/(x^2 - x - 2) + 10/(x + 1) = 3x/(x - 2)
=> (x^2 + 14) / ((x - 2)(x + 1)) + 10/(x + 1) = 3x/(x - 2)

Next, we multiply through by the common denominator (x - 2)(x + 1) to clear the fractions:

(x^2 + 14) + 10(x - 2) = 3x(x + 1)
=> x^2 + 14 + 10x - 20 = 3x^2 + 3x
=> x^2 + 14 + 10x - 20 = 3x^2 + 3x
=> x^2 + 10x - 6 = 3x^2 + 3x

Now, we combine like terms and get all terms on one side of the equation:

0 = 2x^2 + 3x - 20

Next, we set the quadratic equation to zero and factor:

2x^2 + 3x - 20 = 0
=> (2x - 5)(x + 4) = 0

Solving for x, we get two possible solutions:

2x - 5 = 0 => 2x = 5 => x = 5/2
x + 4 = 0 => x = -4

Therefore, the solutions to the given equation are x = 5/2 and x = -4.