SOLUTION: solve (1)/(x-2)-(1)/(x+2)=5

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Question 167716: solve (1)/(x-2)-(1)/(x+2)=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%281%29%2F%28x-2%29-%281%29%2F%28x%2B2%29=5 Start with the given equation.


Multiply every term on both sides by the LCD %28x-2%29%28x%2B2%29. Doing this will eliminate all of the fractions.


x%2B2-%28x-2%29=5%28x-2%29%28x%2B2%29 Multiply and simplify


x%2B2-%28x-2%29=5%28x%5E2-4%29 FOIL


x%2B2-x%2B2=5x%5E2-20 Distribute


4=5x%5E2-20 Combine like terms.


4%2B20=5x%5E2 Add 20 to both sides


24=5x%5E2 Combine like terms


24%2F5=x%5E2 Divide both sides by 5


x=sqrt%2824%2F5%29 or x=-sqrt%2824%2F5%29 Take the square root of both sides.


x=%282%2Asqrt%2830%29%29%2F5 or x=%28-2%2Asqrt%2830%29%29%2F5 Simplify the square root.



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Answer:

So the solutions are x=%282%2Asqrt%2830%29%29%2F5 or x=%28-2%2Asqrt%2830%29%29%2F5