Question 164254
{{{(2/x+1/(x-2))/(1/(x-2)-3/x)}}} Start with the given expression



{{{(cross(x)(x-2)(2/cross(x))+x*cross((x-2))(1/cross((x-2))))/(x*cross((x-2))(1/cross((x-2)))-cross(x)(x-2)(3/cross(x)))}}} Multiply EVERY term by the LCD {{{x(x-2)}}} to clear out the inner denominators



{{{(2(x-2)+x)/(x-3(x-2))}}} Multiply and simplify



{{{(2x-4+x)/(x-3x+6)}}} Distribute



{{{(3x-4)/(-2x+6)}}} Combine like terms.



{{{(3x-4)/(-(2x-6))}}} Factor a negative one from the denominator



{{{-(3x-4)/(2x-6)}}} Simplify



So {{{(2/x+1/(x-2))/(1/(x-2)-3/x)}}} simplifies to {{{-(3x-4)/(2x-6)}}}