SOLUTION: 3/x+2 + 2/x-2 = 8/(x+2)(x-2) Can you please help me solve this?

Algebra ->  Equations -> SOLUTION: 3/x+2 + 2/x-2 = 8/(x+2)(x-2) Can you please help me solve this?      Log On


   

Question 94312This question is from textbook Blitzer
: 3/x+2 + 2/x-2 = 8/(x+2)(x-2)
Can you please help me solve this? This question is from textbook Blitzer

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28x%2B2%29+%2B+2%2F%28x-2%29+=+8%2F%28x%2B2%29%28x-2%29 Start with the given equation


Multiply both sides by the LCD %28x%2B2%29%28x-2%29

3%28x-2%29+%2B+2%28x%2B2%29+=+8 Distribute and multiply

3x-6+%2B+2x%2B4+=+8 Distribute again



3x%2B2x%2B4=8%2B6Add 6 to both sides


3x%2B2x=8%2B6-4Subtract 4 from both sides


5x=8%2B6-4 Combine like terms on the left side


5x=10 Combine like terms on the right side


x=%2810%29%2F%285%29 Divide both sides by 5 to isolate x



x=2 Reduce

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Answer:
So our possible answer is x=2


However, we must check this answer


3%2F%28x%2B2%29+%2B+2%2F%28x-2%29+=+8%2F%28x%2B2%29%28x-2%29 Start with the given equation

3%2F%282%2B2%29+%2B+2%2F%282-2%29+=+8%2F%282%2B2%29%282-2%29 Plug in x=2

3%2F4+%2B+2%2F0+=+8%2F0 Simplify the denominators


Since x=2 makes two fractions have a denominator of zero, the possible solution x=2 is not valid. So there are no solutions.