Question 236420
{{{2/(x-3) - 4/(x+3) = 8/(x^2-9)}}} Start with the given equation.



{{{2/(x-3) - 4/(x+3) = 8/((x-3)(x+3))}}} Factor the last denominator.



{{{cross((x-3))(x+3)(2/cross((x-3))) - (x-3)cross((x+3))(4/cross((x+3))) = cross((x-3)(x+3))(8/(cross((x-3)(x+3))))}}} Multiply EVERY term by the LCD {{{(x-3)(x+3)}}} to clear out the fractions.



{{{(x+3)2-(x-3)4=8}}} Simplify



{{{2(x+3)-4(x-3)=8}}} Rearrange the terms.



{{{2x+6-4x+12=8}}} Distribute.



{{{-2x+18=8}}} Combine like terms on the left side.



{{{-2x=8-18}}} Subtract {{{18}}} from both sides.



{{{-2x=-10}}} Combine like terms on the right side.



{{{x=(-10)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}.



{{{x=5}}} Reduce.



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Answer:


So the solution is {{{x=5}}}