Question 536092
<pre>

{{{4/(x^2+7x+6)}}} - {{{6x/(x^2+4x+3)}}} + {{{(x+4)/(x^2+9x+18)}}}

{{{4/((x+1)(x+6))}}} - {{{6x/((x+1)(x+3))}}} + {{{(x+4)/((x+3)(x+6))}}}

{{{4/((x+1)(x+6))}}}·{{{red(((x+3))/((x+3)))}}} - {{{6x/((x+1)(x+3))}}}·{{{red(((x+6))/((x+6)))}}} + {{{(x+4)/((x+3)(x+6))}}}·{{{red(((x+1))/((x+1)))}}}

{{{(4(x+3))/((x+1)(x+6)(x+3))}}} - {{{(6x(x+6))/((x+1)(x+3)(x+6))}}} + {{{((x+4)(x+1))/((x+3)(x+6)(x+1))}}}

{{{(4(x+3)-6x(x+6)+(x+4)(x+1))/((x+1)(x+6)(x+3))}}}

So you got this far.  Remove all the parentheses on top by using
FOIL and the distributive principle:

{{{(4x+12-6x^2-36x+(x^2+5x+4))/((x+1)(x+6)(x+3))}}}

{{{(4x+12-6x^2-36x+x^2+5x+4)/((x+1)(x+6)(x+3))}}}

Collect all like terms in the top and arrange them in descending order:

{{{(-5x^2-27x+16)/((x+1)(x+6)(x+3))}}}

Edwin</pre>