Solve for x : 1/(x^2+6x+9) + 1/(x+3) = 4/9

We notice that the denominator of the first ratio is the
result of expanding the square (x+3)^2.

We've applied the
formula:

(a+b)^2 = a^2 + 2ab +
b^2

So, x^2+6x+9 =
x^2+2*3*x+(3)^2

We'll re-write the
equation:

1/(x+3)^2 + 1/(x+3) =
4/9

The least common denominator is
9(x+3)^2.

We'll multiply the first ratio by 9, the second
ratio by 9(x+3) and the third ratio by (x+3)^2.

We'll
re-write the equation, without denominators.

9 + 9(x+3) =
4(x+3)^2

We'll remove the brackets from the left side and
we'll expand the square from the right side:

9 + 9x + 27 =
4x^2 + 24x + 36

We'll subtract 4x^2 + 24x + 36 both
sides:

9 + 9x + 27 - 4x^2 - 24x - 36 =
0

We'll combine like terms:

-
4x^2 - 15x = 0

We'll factorize by
-x:

-x(4x + 15) = 0

We'll set
each factor as zero:

-x = 0

x
= 0

4x + 15 = 0

We'll subtract
15:

4x = -15

We'll divide by
4:

x =
-15/4.

The solutions of the equation are:
{-15/4 ; 0}.