Solve the equation (x+1)/(x+2) + (x+2)/(x+3)=7/6.

We notice that the fractions don't have the same
denominator, therefore they cannot be added until they have the same
denominator.

The least common denominator of all fractions
in the given expression is:

LCD =
6(x+2)(x+3)

We'll multiply the first fraction by 6(x+3),
the 2nd fraction by 6(x+2) and the 3rd fraction by
(x+2)(x+3).

6(x+3)(x+1) + 6(x+2)^2 =
7(x+2)(x+3)

We'll remove the
brackets:

6x^2 + 24x + 18 + 6x^2 + 24x + 24 = 7x^2 + 35x +
42

We'll combine like
terms:

12x^2 + 48x + 42 = 7x^2 + 35x +
42

We'll subtract 7x^2 + 35x + 42 both
sides:

12x^2 + 48x + 42 - 7x^2 - 35x - 42 =
0

We'll eliminate like
terms:

5x^2 - 13x = 0

We'll
factorize by x:

x*(5x - 13) =
0

We'll cancel each factor;

x
= 0

5x - 13 = 0

5x = 13
=> x = 13/5

The solutions of the given
equation are valid since they make the fractions posssible, therefore the values of
solutions are: {0 ; 13/5}.