6/(x) + 6/(x + 1) = 5

Multiplying every term by x(x + 1) to clear the fractions:

6(x + 1) + 6x = 5x(x + 1)

Expand and simplify:

6x + 6 + 6x = 5x^2 + 5x

Combine like terms:

12x + 6 = 5x^2 + 5x

Rearrange the equation to set it equal to zero:

5x^2 - 7x - 6 = 0

Factor the quadratic equation:

(5x + 3)(x - 2) = 0

Setting each factor equal to zero:

5x + 3 = 0 or x - 2 = 0

Solving for x:

x = -3/5 or x = 2

Therefore, the solutions are x = -3/5 or x = 2.