Solve the following equation.
\[
\frac{1}{x+1}+\frac{9}{x+3}=\frac{2}{x^{2}+4 x+3}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is \{\} .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The solution set is $\{x \mid x \neq$
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
c. The solution set is $\varnothing$.
Answer
Final Answer: The solution set is \(\boxed{\varnothing}\).
Step 1 ：The given equation is a rational equation. To solve it, we need to clear the fractions by multiplying each term by the least common denominator (LCD) of all the fractions. The LCD of the fractions is the product of \((x+1)\), \((x+3)\), and \((x^2+4x+3)\).
Step 2 ：After clearing the fractions, we will get a quadratic equation which we can solve by factoring or using the quadratic formula.
Step 3 ：However, after simplifying the equation, we find that there are no solutions. This means that the original equation has no solutions.
Step 4 ：Final Answer: The solution set is \(\boxed{\varnothing}\).
