Question 669916
{{{9/(x-3) - 8/(x+3) = 6(1/(x^2+9))}}}
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Multiply the entire equation by {{{x^2 + 9}}}
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{{{(9/(x-3))(x^2+9) - (8/(x+3))(x^2+9) = (6/(x^2+9))(x^2+9))}}}
is the same as
{{{(9/(x-3))(x+3)(x-3) - (8/(x+3))(x+3)(x-3) = (6/(x^2+9))(x^2+9))}}}
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Cancel out terms
{{{9(x+3) - 8(x-3) = 6}}}
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Distribute
9x + 27 - 8x + 24 = 6
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Combine like terms
x = 6 - 27 - 24
{{{highlight_green(x = -45)}}}
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Check
{{{(9/(-45-3)) - 8/(-45+3) = 6/(-45^2 + 9)}}}
{{{9/-48 - 8/-42 = 6/2034}}}
{{{-378/2016 - -384/2016 = 6/2016 = .0029}}}
{{{6/2034 =  .0029}}}
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