To solve this equation, first we need to simplify the left side of the equation by factoring both the numerator and the denominator:

(x^2 - 10x + 15) / (x^2 - 6x + 15) = 3x / (x^2 - 8x + 15)

Factoring the numerator and the denominator on the left side, we get:

((x - 5)(x - 3)) / ((x - 3)(x - 5)) = 3x / (x - 3)(x - 5)

Now, we can cancel out the common factors in the numerator and the denominator:

1 = 3x

Now, we can solve for x:

1 = 3x
x = 1/3

Thus, the solution to the equation is x = 1/3.