Question 198865

{{{(x)/(x^2-4)+(2)/(x-2)=(1)/(x+2)}}} Start with the given equation.



{{{(x)/((x+2)(x-2))+(2)/(x-2)=(1)/(x+2)}}} Factor the first denominator.



{{{cross((x+2)(x-2))((x)/cross((x+2)(x-2)))+cross((x-2))(x+2)((2)/cross((x-2)))=(x-2)cross((x+2))((1)/cross((x+2)))}}} 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)=1(x-2)}}} Simplify



{{{x+2x+4=x-2}}} Distribute.



{{{3x+4=x-2}}} Combine like terms on the left side.



{{{3x=x-2-4}}} Subtract {{{4}}} from both sides.



{{{3x-x=-2-4}}} Subtract {{{x}}} from both sides.



{{{2x=-2-4}}} Combine like terms on the left side.



{{{2x=-6}}} Combine like terms on the right side.



{{{x=(-6)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=-3}}} Reduce.



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Answer:


So the solution is {{{x=-3}}}