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

To solve the given equation, we can follow these steps:

1. Start by multiplying both sides of the equation by the common denominator, which is (x + 6)(x + 1). This will eliminate the fractions and make the equation easier to solve.

(x + 6)(x + 1) * (5/(x + 6)) + (x + 6)(x + 1) * (2/(x^2 + 7x + 6)) = (x + 6)(x + 1) * (3/(x + 1))

Simplifying each term separately:
5(x + 1) + 2 = 3(x + 6)

2. Now, distribute the numbers and simplify each side of the equation:

5x + 5 + 2 = 3x + 18

Combine like terms:
5x + 7 = 3x + 18

3. Next, get all the variables on one side and the constants on the other side. Subtract 3x from both sides:

5x - 3x + 7 = 3x - 3x + 18

Simplify:
2x + 7 = 18

4. Subtract 7 from both sides to isolate the variable:

2x + 7 - 7 = 18 - 7

Simplify:
2x = 11

5. Finally, divide both sides by 2 to solve for x:

(2x) / 2 = 11 / 2

Simplify:
x = 11 / 2

Therefore, the solution to the equation 5/(x + 6) + 2/(x^2 + 7x + 6) = 3/(x + 1) is x = 11 / 2.