SOLUTION: could you please help me with this: 6/x+3 - 3/x+6 = 4/x+3 Could you show me the steps as well as your answer please? Thank you

Algebra ->  Equations -> SOLUTION: could you please help me with this: 6/x+3 - 3/x+6 = 4/x+3 Could you show me the steps as well as your answer please? Thank you      Log On


   

Question 92406: could you please help me with this:
6/x+3 - 3/x+6 = 4/x+3
Could you show me the steps as well as your answer please?
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%28x%2B3%29+-+3%2F%28x%2B6%29+=+4%2F%28x%2B3%29 Start with the given equation

Multiply both sides by the LCD

6%28x%2B6%29+-+3%28x%2B3%29+=4%28x%2B6%29 Distribute and multiply


6x%2B36-3x-9=4x%2B24 Distribute again




3x%2B36-9=4x%2B24 Combine the variable terms 6x and -3x on the left side to get 3x



3x%2B27=4x%2B24 Combine the constant terms 36 and -9 on the left side to get 27



3x=4x%2B24-27 Subtract 27 from both sides


3x-4x=24-27 Subtract 4x from both sides



-1+x=24-27 Combine like terms 3+x and -4+x on the left side to get -1+x




-1+x=-3 Combine like terms -27 and 24 on the left side to get -3





x=%28-3%29%2F%28-1%29 Now divide both sides by -1 to isolate and solve for x


x=+3 Reduce



So our answer is
x=+3




Check:
6%2F%28x%2B3%29+-+3%2F%28x%2B6%29+=+4%2F%28x%2B3%29 Start with the given equation

6%2F%283%2B3%29+-+3%2F%283%2B6%29+=+4%2F%283%2B3%29 plug in the answer x=3

6%2F6+-+3%2F9+=+4%2F6 Add

%283%2F3%29%286%2F6%29+-+%282%2F2%29%283%2F9%29+=+4%2F6 Multiply both fractions by a form of 1 to make both denominators equal

18%2F18+-+6%2F18+=+4%2F6 Multiply

12%2F18+=+4%2F6 Subtract

2%2F3+=+2%2F3 Reduce both sides. So our answer is verified