Question 167707
{{{(12)/(x)-(12)/(x-1)=-1}}} Start with the given equation.



{{{cross(x)(x-1)((12)/cross(x))-x*cross((x-1))((12)/cross((x-1)))=x(x-1)(-1)}}} Multiply <font size="4"><b>EVERY</b></font> term on both sides by the LCD {{{x(x-1)}}}. Doing this will eliminate all of the fractions.



{{{12(x-1)-12x=-x(x-1)}}} Multiply and simplify (I also rearranged some terms)



{{{12x-12-12x=-x^2+x}}} Distribute



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



{{{0=-x^2+x+12}}} Add 12 to both sides.



{{{(-x+4)(x+3)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{-x+4=0}}} or  {{{x+3=0}}} 


{{{x=4}}} or  {{{x=-3}}}    Now solve for x in each case



So our answers are 


 {{{x=4}}} or  {{{x=-3}}}