Question 167716

{{{(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 <font size="4"><b>every</b></font> 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}}}