Tìm x:

To solve the equation, we can start by simplifying both sides of the equation.

On the left side, we have:
(x+1)(x+3) + 3/(x+3)(x+6) + 4/(x+6)(x+10)

Expanding the first term:
(x^2 + 4x + 3) + 3/(x+3)(x+6) + 4/(x+6)(x+10)

Expanding the second term:
(x^2 + 4x + 3) + 3/((x+3)(x+6)) + 4/(x+6)(x+10)

Expanding the third term:
(x^2 + 4x + 3) + 3/((x+3)(x+6)) + 4/((x+6)(x+10))

On the right side, we have:
9/(x+1)(x+10)

Now, we can combine the fractions on the left side by finding a common denominator.

The common denominator is (x+3)(x+6)(x+10).

Multiplying the first term by (x+6)(x+10)/(x+6)(x+10):
(x^2 + 4x + 3)(x+6)(x+10)/(x+6)(x+10)

Multiplying the second term by (x+10)/(x+10):
3(x+10)/(x+3)(x+6)(x+10)

Multiplying the third term by (x+3)/(x+3):
4(x+3)/(x+3)(x+6)(x+10)

Combining the fractions on the left side:
[(x^2 + 4x + 3)(x+6)(x+10) + 3(x+10) + 4(x+3)] / (x+3)(x+6)(x+10)

Now, we can set the left side equal to the right side and solve for x:

[(x^2 + 4x + 3)(x+6)(x+10) + 3(x+10) + 4(x+3)] / (x+3)(x+6)(x+10) = 9/(x+1)(x+10)

Multiplying both sides by (x+3)(x+6)(x+10)(x+1)(x+10) to clear the denominators:
[(x^2 + 4x + 3)(x+6)(x+10) + 3(x+10) + 4(x+3)](x+1)(x+10) = 9(x+3)(x+6)(x+1)(x+10)

Expanding both sides:
[(x^2 + 4x + 3)(x^2 + 16x + 60) + 3(x+10) + 4(x+3)](x+1)(x+10) = 9(x^2 + 7x + 18)(x+10)

Simplifying both sides:
(x^2 + 4x + 3)(x^2 + 16x + 60) + 3(x+10) + 4(x+3) = 9(x^2 + 7x + 18)

Expanding both sides:
x^4 + 20x^3 + 123x^2 + 252x + 180 + 3x + 30 + 4x + 12 = 9x^2 + 63x + 162

Combining like terms:
x^4 + 20x^3 + 123x^2 + 259x + 222 = 9x^2 + 63x + 162

Moving all terms to one side:
x^4 + 20x^3 + 114x^2 + 196x + 60 = 0

Unfortunately, this equation cannot be easily solved algebraically. It may require numerical methods or approximation techniques to find the solutions.