Question 191958
{{{6/(x^2-9)- 1/(x-3) = 1}}} Start with the given equation.



{{{6/((x+3)(x-3))- 1/(x-3) = 1}}} Factor the first denominator



{{{cross((x+3)(x-3))(6/(cross((x+3)(x-3))))- (x+3)cross((x-3))(1/cross((x-3))) = 1(x+3)(x-3)}}} Multiply EVERY term by the LCD {{{(x+3)(x-3)}}}



{{{6-(x+3)=(x+3)(x-3)}}} Multiply and simplify 



{{{6-x-3=(x+3)(x-3)}}} Distribute



{{{-x+3=(x+3)(x-3)}}} Combine like terms.



{{{-x+3=x^2-9}}} FOIL



{{{0=x^2-9+x-3}}} Get everything to the right side



{{{0=x^2+x-12}}} Combine like terms.



{{{0=(x+4)(x-3)}}} Factor



{{{x+4=0}}} or {{{x-3=0}}} Set each factor equal to zero



{{{x=-4}}} or {{{x=3}}} Solve for "x" in each case




So the <i>possible</i> solutions are {{{x=-4}}} or {{{x=3}}}



However, if you plug in {{{x=3}}}, you'll see that a division by zero occurs. So {{{x=3}}} is NOT a solution (it's not even in the domain)




So the only solution is {{{x=-4}}}