Question 145491
{{{(1-2/x)/(x-4/x)}}} Start with the given expression



{{{(x(1-2/x))/(x(x-4/x))}}} Multiply <b>both</b> the numerator and the denominator by the LCD {{{x}}}



{{{(x(1)-cross(x)(2/cross(x)))/(x(x)-cross(x)(4/cross(x)))}}} Distribute. Notice how the inner denominators cancel



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


{{{(x-2)/((x-2)*(x+2))}}} Factor {{{x^2-4}}} to get {{{(x-2)*(x+2)}}}.



{{{(highlight(x-2))/(highlight(x-2)(x+2))}}} Highlight the common terms. 



{{{(cross(x-2))/(cross(x-2)(x+2))}}} Cancel out the common terms. 



{{{1/((x+2))}}} Simplify. 



So {{{(1-2/x)/(x-4/x)}}} simplifies to {{{1/((x+2))}}}.



In other words, {{{(1-2/x)/(x-4/x)=1/((x+2))}}} where {{{x<>0}}}, {{{x<>-2}}}, or {{{x<>2}}}