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

The common denominator for the fractions on the left side would be (x-3)(x-1). Multiplying each fraction by the necessary factors to achieve this common denominator, we get:

10(x-1)/(x-3)(x-1) + (3x-6)(x-3)/(x-3)(x-1) = 3/(x-3)(x-1)

Now, combine the fractions on the left side:

(10x-10 + 3x^2 - 9x)/(x-3)(x-1) = 3/(x-3)(x-1)

Simplify the numerator:

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

Now, multiply both sides by (x-3)(x-1) to get rid of the denominators:

3x^2 + x - 10 = 3

Rearrange the equation:

3x^2 + x - 13 = 0

Now, solve for x. You can do this by factoring the quadratic equation or using the quadratic formula:

x = (-1 ± √(1 + 4313)) / (2*3)
x = (-1 ± √(1 + 156)) / 6
x = (-1 ± √157) / 6

So the solutions to the equation are:

x = (-1 + √157) / 6 and x = (-1 - √157) / 6