Question 908849

if you have:
{{{1/x - 1/x+4 = 1/3}}}

{{{cross(1/x )- cross(1/x)+4 = 1/3}}}

{{{4 = 1/3}}} ...since {{{4 <> 1/3}}}, there is no solution


but, if you have:

{{{ 1/x - 1/(x+4) = 1/3 }}} , than find common denominator


{{{1(x+4)/(x(x+4)) - 1*x/(x(x+4)) = 1/3}}}


{{{((x+4)- x)/(x(x+4)) = 1/3}}}

{{{ 4/(x(x+4)) = 1/3}}}....cross multiply

{{{4*3 = 1*(x(x+4))}}}

{{{12 = x^2+4x}}}

{{{0 = x^2+4x-12}}} or

{{{x^2+4x-12=0}}} ...solve for {{{x}}} by factoring; write {{{4x}}} as {{{6x-2x}}} 

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

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

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

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


solutions:

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

if {{{ x+6 = 0 }}} => {{{x=-6}}}