Question 191061
I'm assuming that the equation is {{{(3x)/(x^2-1)=5/x}}}.



{{{(3x)/(x^2-1)=5/x}}} Start with the given equation



{{{(3x)(x)=5(x^2-1)}}} Cross multiply



{{{3x^2=5x^2-5}}} Distribute and multiply



{{{3x^2-5x^2=-5}}} Subtract {{{5x^2}}} from both sides



{{{-2x^2=-5}}} Combine like terms.



{{{x^2=-5/(-2)}}} Divide both sides by -2



{{{x^2=5/2}}} Reduce



{{{x=""+-sqrt(5/2)}}} Take the square root of both sides




{{{x=sqrt(5/2)}}} or {{{x=-sqrt(5/2)}}} Break up the "plus/minus" to form 2 separate equations.



{{{x=sqrt(10)/2}}} or {{{x=-sqrt(10)/2}}} Simplify the square root.



So the solutions are {{{x=sqrt(10)/2}}} or {{{x=-sqrt(10)/2}}}