Question 947128
{{{x/(4x-8)-(x+1)/(x^2 + 2x-8)}}}


{{{x/(4(x-2))-(x+1)/(x^2 -2x+ 4x-8)}}}


{{{x/(4(x-2))-(x+1)/((x^2 -2x)+ (4x-8))}}}


{{{x/(4(x-2))-(x+1)/(x(x -2)+ 4(x-2))}}}


{{{x/(4(x-2))-(x+1)/((x+4)(x-2))}}}


{{{x(x+4)/(4(x-2)(x+4))-4(x+1)/(4(x+4)(x-2))}}}


{{{(x(x+4)-4(x+1))/(4(x+4)(x-2))}}}


{{{(x^2+cross(4x)-cross(4x)-4)/(4(x+4)(x-2))}}}


{{{(x^2-4)/(4(x+4)(x-2))}}}


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


{{{(cross((x-2))(x+2))/(4(x+4)cross((x-2))))}}}


{{{(x+2)/4(x+4)}}}


a value of {{{x}}} that makes numerator equal to zero will be a real root:

if {{{(x+2)=0}}}=> {{{highlight(x=-2)}}}-> root


restrictions:


exclude a value of {{{x}}} that makes denominator equal to zero

{{{(4x-8)}}}=>{{{4x=8}}}=>{{{x=2}}}
and
if {{{(x+4)=0}}}=> {{{x=-4}}}

so, { {{{x}}} element {{{R}}} : {{{x<>-4}}} and {{{x<>2}}} }



{{{ graph( 600, 600, -10, 10, -10, 10, (x+2)/4(x+4)) }}}