Question 130239
{{{ 4/(x-1)= (x-1)/9 }}} Start with the given equation



{{{ 4= (x-1)(x-1)/9 }}} Multiply both sides by x-1


{{{ 4*9= (x-1)(x-1) }}} Multiply both sides by 9



{{{ 36= (x-1)(x-1) }}} Multiply



{{{ 36= x^2-2x+1 }}} Foil the right side



{{{ 0= x^2-2x-35 }}} Subtract 36 from both sides



{{{ 0=(x-7)(x+5)}}} Factor the right side



Set each factor equal to zero


{{{x-7=0}}} or {{{x+5=0}}}


Solve for x in each case


{{{x=7}}} or {{{x=-5}}}



So our answers are 



{{{x=-5}}} or {{{x=7}}}