<PRE><B>Question 143036</B>
{{{1/(4x+12)-1/(x^2-9)=5/(x-3)}}} Start with the given equation



{{{1/(4(x+3))-1/((x-3)(x+3))=5/(x-3)}}} Factor {{{4x+12}}} to get {{{4(x+3)}}}. Factor {{{x^2-9}}} to get {{{(x-3)(x+3)}}}



So  the LCD is {{{4(x+3)(x-3)}}}



{{{4(x+3)(x-3)(1/(cross(4(x+3)))-1/(cross((x-3)(x+3))))=4(x+3)cross((x-3))(5/cross(x-3))}}} Multiply both sides by the LCD {{{4(x+3)(x-3)}}} to clear the fractions



{{{(x-3)-4=20(x+3)}}} Distribute and multiply



{{{x-3-4=20x+60}}} Distribute again



{{{x-7=20x+60}}} Combine like terms on the left side



{{{x=20x+60+7}}}Add 7 to both sides



{{{x-20x=60+7}}} Subtract 20x from both sides



{{{-19x=60+7}}} Combine like terms on the left side



{{{-19x=67}}} Combine like terms on the right side



{{{x=(67)/(-19)}}} Divide both sides by -19 to isolate x




{{{x=-67/19}}} Reduce


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Answer:

So our answer is {{{x=-67/19}}}  (which is approximately {{{x=-3.5263}}} in decimal form)
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