Question 771989

{{{x/(3sqrt(2X-3)) - 1/(sqrt(2x-3)) = 1/3}}}


{{{x/(3sqrt(2X-3)) - (1*3)/(3sqrt(2x-3)) = 1/3}}}


{{{x/(3sqrt(2X-3)) - 3/(3sqrt(2x-3)) = 1/3}}}


{{{(x- 3)/(3sqrt(2x-3)) = 1/3}}}.....cross multiply


{{{(x- 3)*3 = 1(3sqrt(2x-3))}}}


{{{(x- 3)*cross(3) = cross(3)sqrt(2x-3)}}}


{{{(x- 3) = sqrt(2x-3)}}}.......square both sides


{{{(x- 3)^2 = (sqrt(2x-3))^2}}}


{{{x^2- 6x+9 = 2x-3}}}


{{{x^2- 6x+9 -2x+3=0}}}


{{{x^2-8x+12=0}}}.....write {{{-8x}}} as {{{-2x-6x}}}


{{{x^2-2x-6x+12=0}}}....group


{{{(x^2-2x)-(6x-12)=0}}}

{{{x(x-2)-6(x-2)=0}}}

{{{(x-6)(x-2) = 0}}}

solutions:

if {{{(x-6) = 0}}}=> {{{x=6}}}

if {{{(x-2) = 0}}}=> {{{x=2}}}