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Question 167716: solve (1)/(x-2)-(1)/(x+2)=5: solve (1)/(x-2)-(1)/(x+2)=5
Answer by jim_thompson5910(9862) About Me  (Show Source):
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(1)/(x-2)-(1)/(x+2)=5 Start with the given equation.


cross((x-2))(x+2)((1)/cross((x-2)))-(x-2)cross((x+2))((1)/cross((x+2)))=(x-2)(x+2)(5) Multiply every term on both sides by the LCD (x-2)(x+2). Doing this will eliminate all of the fractions.


x+2-(x-2)=5(x-2)(x+2) Multiply and simplify


x+2-(x-2)=5(x^2-4) FOIL


x+2-x+2=5x^2-20 Distribute


4=5x^2-20 Combine like terms.


4+20=5x^2 Add 20 to both sides


24=5x^2 Combine like terms


24/5=x^2 Divide both sides by 5


x=sqrt(24/5) or x=-sqrt(24/5) Take the square root of both sides.


x=(2*sqrt(30))/5 or x=(-2*sqrt(30))/5 Simplify the square root.



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Answer:

So the solutions are x=(2*sqrt(30))/5 or x=(-2*sqrt(30))/5