SOLUTION: Solve the equation. Give all solutions (real or complex) 2/(x+1) - 4/(x+2) = 3x/x^2 + 3x+2

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve the equation. Give all solutions (real or complex) 2/(x+1) - 4/(x+2) = 3x/x^2 + 3x+2      Log On


   

Question 733607: Solve the equation. Give all solutions (real or complex)
2/(x+1) - 4/(x+2) = 3x/x^2 + 3x+2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you meant 2/(x+1) - 4/(x+2) = 3x/(x^2 + 3x+2) or 2%2F%28x%2B1%29+-+4%2F%28x%2B2%29+=+3x%2F%28x%5E2+%2B+3x%2B2%29
Since %28x%2B1%29%28x%2B2%29=x%5E3%2B3x%2B2 I would multiply both sides of the equation times that to get

That simplifies to
2%28x%2B2%29-4%28x%2B1%29=3x
Doing the indicated multiplications we get
2x%2B4-4x-4=3x which simplifies to
2x-4x=3x --> 2x-4x%2B4x-2x=3x%2B4x-2x --> 0=5x --> highlight%28x=0%29
There are no more solutions.
Verification:
substituting 0 for x we get
2%2F1-4%2F2=0%2F2 or 2-2=0
So x=0 is a solution.