Question 187683
{{{(3x)/(x^2-1)=5/x}}} Start with the given equation.



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



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



{{{3x^2=5x^2-5}}} 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)}}} or {{{x=-sqrt(5/2)}}} Take the square root of both sides (keep in mind that there are two possible options here)



{{{x=sqrt(5)/sqrt(2)}}} or {{{x=-sqrt(5)/sqrt(2)}}} Break up the square root.



{{{x=(sqrt(5)*sqrt(2))/(sqrt(2)*sqrt(2))}}} or {{{x=-(sqrt(5)*sqrt(2))/(sqrt(2)*sqrt(2))}}} Multiply the numerator and denominator by {{{sqrt(2)}}} (to rationalize the denominator)



{{{x=sqrt(10)/2}}} or {{{x=-sqrt(10)/2}}} Combine the roots and multiply


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Answer:



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