SOLUTION: Can you please explain the steps to solving this problem? Thank You! x+2/x+1= 1/x+1 + 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please explain the steps to solving this problem? Thank You! x+2/x+1= 1/x+1 + 2      Log On


   

Question 88737: Can you please explain the steps to solving this problem? Thank You!
x+2/x+1= 1/x+1 + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B2%29%2F%28x%2B1%29=+1%2F%28x%2B1%29+%2B+2 Does your problem look like this?

%28x%2B1%29%28%28x%2B2%29%2F%28x%2B1%29%29=+%28x%2B1%29%281%2F%28x%2B1%29+%2B+2%29 Multiply both sides by the LCD x%2B1

x%2B2=+1%2B2%28x%2B1%29 Distribute

x%2B2=+1%2B2x%2B2 Distribute again

x%2B2=2x%2B3 Combine like terms

x=2x%2B1 Subtract 2 from both sides

-x=1 Subtract 2x from both sides

x=-1 Multiply both sides by -1

Check:
%28-1%2B2%29%2F%28-1%2B1%29=+1%2F%28-1%2B1%29+%2B+2 Plug in x=-1

1%2F0=+1%2F0+%2B+2 Since dividing by zero is not possible, there are no solutions.