did i solve this correctly?

Question

Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

(x + 3)/(x + 1) + 2/(x²+ x)=0

 

(x+3)/(x+1) + 2/x(x+1)=0

 

(x+3)(x)+2=0(x+1)(x)

 

x^₂+3x+2 =0

(x+1)(x+2)=0

x+1 = 0 or x+2 = 0

 

x=-1 does not work in the original equation

x=-2 works in the original equation

 

ANSWER is x=-2

 

 

Answer 1

yes, you did an excellent job, especially noting the domain restriction of the original problem (x can't be 0 or -1), then getting a common denominator, and finally discarding one of the zeros obtained when you set the numerator polynomial to zero.