Question 196634
{{{3 / (x - 3) + 6 / (x^2) = 0}}} Start with the given equation.



{{{x^2cross((x - 3))(3/cross((x - 3))) + cross(x^2)(x-3)(6/cross(x^2)) = 0(x^2(x-3))}}} Multiply EVERY term by the LCD {{{x^2(x-3)}}} to clear out the fractions.



{{{x^2(3)+(x-3)(6)=0}}} Multiply and simplify



{{{3x^2+6(x-3)=0}}} Rearrange the terms.



{{{3x^2+6x-18=0}}} Distribute



Notice we have a quadratic in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=6}}}, and {{{C=-18}}}



Let's use the quadratic formula to solve for x



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(6) +- sqrt( (6)^2-4(3)(-18) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=6}}}, and {{{C=-18}}}



{{{x = (-6 +- sqrt( 36-4(3)(-18) ))/(2(3))}}} Square {{{6}}} to get {{{36}}}. 



{{{x = (-6 +- sqrt( 36--216 ))/(2(3))}}} Multiply {{{4(3)(-18)}}} to get {{{-216}}}



{{{x = (-6 +- sqrt( 36+216 ))/(2(3))}}} Rewrite {{{sqrt(36--216)}}} as {{{sqrt(36+216)}}}



{{{x = (-6 +- sqrt( 252 ))/(2(3))}}} Add {{{36}}} to {{{216}}} to get {{{252}}}



{{{x = (-6 +- sqrt( 252 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (-6 +- 6*sqrt(7))/(6)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-6)/(6) +- (6*sqrt(7))/(6)}}} Break up the fraction.  



{{{x = -1 +- sqrt(7)}}} Reduce.  



{{{x = -1+sqrt(7)}}} or {{{x = -1-sqrt(7)}}} Break up the expression.  



So the solutions are {{{x = -1+sqrt(7)}}} or {{{x = -1-sqrt(7)}}} 



which approximate to {{{x=1.646}}} or {{{x=-3.646}}}