Question 879376
What you said both ways is still not precise, but I will try to guess what you mean.


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


Looking for a lowest or simplest common denominator, x(x-3) occurs.  Note that -(x-3)=3-x, so I am ignoring the negative 1 as part of common denominator.



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

{{{(x^2+4x(x-3))/(x^2-3x-x(-1))}}}

{{{(x^2+4x^2-12x)/(x^2-3x+x)}}}

{{{(5x^2-12x)/(x^2-2x)}}}

See the common factor of x in numerator and denominator,

{{{highlight((5x-12)/(x-2))}}}