Question 411220
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Almost certainly, your equation is 18/(x-3)+18/(x+3)=8.  (If you are working a problem like this, then you should be far enough in your study of algebra to know that proper use of parentheses is important!)<br>
Inspection and a little logical reasoning and mental arithmetic show that x=6 is a solution.  However, formal algebra shows that there are two solutions....<br>
{{{18/(x-3)+18/(x+3)=8}}}<br>
Multiply both sides by {{{(x-3)(x+3)}}} to clear fractions:<br>
{{{18(x+3)+18(x-3)=8(x+3)(x-3)}}}
{{{18x+54+18x-54=8(x^2-9)=8x^2-72}}}<br>
{{{36x=8x^2-72}}}
{{{8x^2-36x-72=0}}}
{{{2x^2-9x-18=0}}}
{{{(x-6)(2x+3)=0}}}<br>
{{{x=6}}} or {{{x=-3/2}}}<br>
ANSWERS: 6 and -3/2