SOLUTION: Please solve and give all the steps for this problem: (-2x)/(x+2) + (x)/(3) + (4)/(x+2)

Algebra ->  Expressions-with-variables -> SOLUTION: Please solve and give all the steps for this problem: (-2x)/(x+2) + (x)/(3) + (4)/(x+2)      Log On


   

Question 735159: Please solve and give all the steps for this problem:
(-2x)/(x+2) + (x)/(3) + (4)/(x+2)
Answer by Susan-math(40) About Me  (Show Source):
You can put this solution on YOUR website!
Least common denominator is 3(x+2)
To get that in %28-2x%29%2F%28x%2B2%29 multiply numerator and denominator by 3/3 to get
3%28-2x%29%2F%283%28x%2B2%29%29=%28-6x%29%2F%283%28x%2B2%29%29
For x%2F3 multiply by %28x%2B2%29%2F%28x%2B2%29 and get %28x%28x%2B2%29%29%2F%283%28x%2B2%29%29
For 4%2F%28x%2B2%29 multiply by 3/3 to get 12%2F%283%28x%2B2%29%29
So we are adding numerators %28-6x%29+%2B+x%28x%2B2%29+%2B+12+=+-6x+%2Bx%5E2%2B+2x+%2B+12+=+x%5E2-4x%2B12+
Factor that to get %28x-6%29%28x%2B2%29
So we have %28%28x-6%29%28x%2B2%29%29%2F%283%28x%2B2%29%29 which we can reduce by canceling the common factor of (x+2) in the numerator and denominator to get
%28x-6%29%2F3