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

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Math

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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}.

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