Question 111373
{{{(x-11)/(x^2-9) - (x-7)/(x^2-3x)}}} Start with the given expression



{{{(x-11)/((x+3)(x-3)) - (x-7)/(x^2-3x)}}} Factor the first denominator



{{{(x-11)/((x+3)(x-3)) - (x-7)/(x(x-3))}}} Factor the second denominator



So in order to combine these fractions, we need the LCD. So to find the LCD, simply pull out the unique factors x, x+3, and x-3 to get the LCD {{{x(x+3)(x-3)}}}. So we want our denominators to get to this term



{{{(x/x)((x-11)/((x+3)(x-3))) - (x-7)/(x(x-3))}}} Multiply the first fraction by {{{x/x}}}



{{{(x^2-11x)/((x+3)(x-3)) - (x-7)/(x(x-3))}}} Multiply the fractions



{{{(x^2-11x)/((x+3)(x-3)) - ((x+3)/(x+3))((x-7)/(x(x-3)))}}} Multiply the second fraction by {{{(x+3)/(x+3)}}}



{{{(x^2-11x)/(x(x+3)(x-3)) - (x^2-4x-21)/(x(x+3)(x-3))}}} Foil and multiply



Since we now have a common denominator of {{{x(x+3)(x-3)}}}, we can combine the fractions



{{{(x^2-11x- (x^2-4x-21))/(x(x+3)(x-3))}}} Combine the fractions 



{{{(x^2-11x- x^2+4x+21)/(x(x+3)(x-3)) }}} Distribute the negative



{{{(-7x+21)/(x(x+3)(x-3))}}} Combine like terms



{{{-7(x-3)/(x(x+3)(x-3))}}} Factor out -7



{{{-7*cross((x-3))/(x(x+3)cross((x-3)))}}} Cancel like terms


{{{-7/(x(x+3))}}} Simplify



So {{{(x-11)/(x^2-9) - (x-7)/(x^2-3x)}}} simplifies to {{{-7/(x(x+3)) }}}