Question 38120
{{{ x/(x-2) + (1-5x)/(x^2 -8x+12) }}}


Since this is addition of two fractions, you must first find a common denominator.  Begin by factoring the second denominator:
{{{ x/(x-2) + (1-5x)/((x-2)*(x-6)) }}}


The LCD must have all factors of the denominators, and this will be (x-2)*(x-6).  The second fraction already has the common denominator, but you will have to multiply the numerator and denominator of the first fraction by the missing factor (x-6).

{{{ (x/(x-2))*((x-6)/(x-6)) + (1-5x)/((x-2)*(x-6)) }}}

{{{ (x(x-6))/((x-2)*(x-6)) +(1-5x)/((x-2)*(x-6)) }}}


DON'T CANCEL ANYTHING --THESE ARE TERMS!!!

Multiply the numerators out and add them together, and divide by the LCD:
{{{ (x^2-6x +1-5x)/((x-2)*(x-6)) }}}

{{{ (x^2 - 11x +1) /((x-2)*(x-6)) }}}


R^2 at SCC