Question 197565
{{{(1-t)/(9-t)=8/(t-9)}}} Start with the given equation.



Take note that {{{t<>9}}} since this causes a division by zero.



{{{(1-t)(t-9)=8(9-t)}}} Cross multiply



{{{t-9-t^2+9t=8(9-t)}}} FOIL
 


{{{t-9-t^2+9t=72-8t}}} Distribute



{{{t-9-t^2+9t-72+8t=0}}} Get everything to one side



{{{-t^2+18t-81=0}}} Combine like terms.



{{{t^2-18t+81=0}}} Multiply EVERY term by -1 to make the leading coefficient positive.



{{{(t-9)^2=0}}} Factor



{{{t-9=0}}} Take the square root of both sides



{{{t=9}}} Add 9 to both sides.



So the <i>possible</i> solution is {{{t=9}}}.




However, we said earlier that {{{t<>9}}}, so {{{t=9}}} is NOT a solution (it's not in the domain).



So there are no solutions.