Question 491476

{{{ 4(x-2)/(x-3)+3/x=(-3)/x(x-3) }}}...common denominator is {{{x(x-3) }}}


{{{ 4x(x-2)/x(x-3)+3(x-3)/x(x-3)=(-3)/x(x-3) }}}


{{{ (4x(x-2)+3(x-3))/x(x-3)=(-3)/x(x-3) }}}


{{{ (4x^2-8x+3x-9)/cross(x(x-3))=(-3)/cross(x(x-3)) }}}


{{{ 4x^2-8x+3x-9=-3 }}}


{{{ 4x^2-5x-9+3=0 }}}


{{{ 4x^2-5x-6=0 }}}

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


{{{x = (-(-5) +- sqrt( (-5)^2-4*4*(-6) ))/(2*4) }}}


{{{x = (5 +- sqrt(25+96))/8 }}}


{{{x = (5 +- sqrt(121))/8 }}}


{{{x = (5 +- 11)/8 }}}

solutions:

{{{x = (5 + 11)/8 }}}

{{{x = 16/8 }}}

{{{highlight(x =2) }}}

or

{{{x = (5- 11)/8 }}}

{{{x = -6/8 }}}

{{{x =highlight(-3/4) }}}