Question 172179
{{{x/(x^2-9)+3/(x^2+6x+9)+3/(6-2x)}}} Start with the given expression



{{{x/((x+3)(x-3))+3/(x^2+6x+9)+3/(6-2x)}}} Factor {{{x^2-9}}} to get {{{(x+3)(x-3)}}}



{{{x/((x+3)(x-3))+3/((x+3)(x+3))+3/(6-2x)}}} Factor {{{x^2+6x+9}}} to get {{{(x+3)(x+3)}}}



{{{x/((x+3)(x-3))+3/((x+3)(x+3))+3/(-2(x-3))}}} Factor {{{6-2x}}} to get {{{2(3-x)=-2(x-3)}}}




{{{x/((x+3)(x-3))+3/((x+3)(x+3))-3/(2(x-3))}}} Reduce




Take note that the LCD is {{{2(x+3)(x+3)(x-3)}}}. So the goal is to get EVERY denominator equal to the LCD



{{{(2x(x+3))/(2(x+3)(x+3)(x-3))+3/((x+3)(x+3))-3/(2(x-3))}}} Multiply the first fraction by {{{(2(x+3))/(2(x+3))}}}



{{{(2x(x+3))/(2(x+3)(x+3)(x-3))+(3*2(x-3))/(2(x+3)(x+3)(x-3))-3/(2(x-3))}}} Multiply the second fraction by {{{(2(x-3))/(2(x-3))}}}



{{{(2x(x+3))/(2(x+3)(x+3)(x-3))+(3*2(x-3))/(2(x+3)(x+3)(x-3))-(3(x+3)(x+3))/(2(x+3)(x+3)(x-3))}}} Multiply the third fraction by {{{((x+3)(x+3))/((x+3)(x+3))}}}



{{{(2x(x+3))/(2(x+3)(x+3)(x-3))+(3*2(x-3))/(2(x+3)(x+3)(x-3))-(3(x^2+6x+9))/(2(x+3)(x+3)(x-3))}}} FOIL



{{{(2x^2+6x)/(2(x+3)(x+3)(x-3))+(6x-18)/(2(x+3)(x+3)(x-3))-(3x^2+18x+27))/(2(x+3)(x+3)(x-3))}}} Distribute



{{{(2x^2+6x+(6x-18)-(3x^2+18x+27))/(2(x+3)(x+3)(x-3))}}} Combine the fractions.



{{{(2x^2+6x+6x-18-3x^2-18x-27)/(2(x+3)(x+3)(x-3))}}} Distribute



{{{(-x^2-6x-45)/(2(x+3)(x+3)(x-3))}}} Combine like terms.



So {{{x/(x^2-9)+3/(x^2+6x+9)+3/(6-2x)}}} combines and simplifies to {{{(-x^2-6x-45)/(2(x+3)(x+3)(x-3))}}}