Question 1152366

{{{4/(x-1)^2-12/(3x-1)^2=3}}}


{{{4(3x-1)^2/((3x-1)^2*(x-1)^2)-12(x-1)^2/((3x-1)^2*(x-1)^2)=3}}}


{{{(4(3x-1)^2-12(x-1)^2)/((3x-1)^2*(x-1)^2)=3}}}


{{{(4(3x-1)^2-12(x-1)^2)=3((3x-1)^2*(x-1)^2)}}}


{{{4(9x^2-6x+1)-12(x^2-2x+1)=3((9x^2-6x+1)*(x^2-2x+1))}}}


{{{36x^2 - 24x + 4-(12x^2 - 24x + 12)=27x^4 - 72x^3 + 66x^2 - 24x + 3}}}


{{{36x^2 - 24x + 4-12x^2 +24x -12=27x^4 - 72x^3 + 66x^2 - 24x + 3}}}


{{{24x^2 - 8=27x^4 - 72x^3 + 66x^2 - 24x + 3}}}


{{{0=27x^4 - 72x^3 + 66x^2-24x^2  - 24x + 3+8}}}


{{{27x^4 - 72x^3 + 42x^2 - 24x + 11=0}}}


{{{(3x^2 + 1) (9x^2 - 24x + 11) = 0}}}



if {{{(3x^2 + 1)  = 0}}}=>{{{3x^2 = -1}}} =>{{{x^2 = -1/3}}}

=>{{{x = sqrt(-1/3)}}}

so, 

solutions:{{{x = i/sqrt(3)}}} or {{{x = -i/sqrt(3)}}} 



if {{{ 9x^2 - 24x + 11 = 0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-(-24) +- sqrt( (-24)^2-4*9*11 ))/(2*9) }}} 

{{{x = (24 +- sqrt( 576-396 ))/18 }}} 

{{{x = (24 +- sqrt( 180))/18 }}} 

{{{x = (24 +- sqrt( 36*5))/18 }}} 

{{{x = (24 +- 6sqrt( 5))/18 }}} 

{{{x = (cross(24)4 +- cross(6)sqrt( 5))/cross(18)3 }}} 


{{{x = (4 +- sqrt( 5))/3 }}}

solutions:

{{{x = 4/3 + sqrt(5)/3}}}


{{{x = 4/3 -sqrt(5)/3}}}