Question 869708
Not well written.  Grouping symbols MUST BE used in the proper positions:


Your step appears to indicate three separate summands:
5/(x^2+5x+6) + 2/x+3 


and as rendered appear this way:
{{{5/(x^2+5x+6)+ 2/x+3 }}}


Maybe that is not what you really have.  Maybe you really have this:
{{{5/(x^2+5x+6)+2/(x+3)}}}.  I will work through part of this one.

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{{{5/((x+2)(x+3))+2/(x+3)}}}, you see LCD is (x+2)(x+3).  Need to multiply the second summand by 1.

{{{5/((x+2)(x+3))+(2/(x+3))((x+2)/(x+2))}}}
{{{(5+2(x+2))/((x+2)(x+3))}}}
{{{(5+2x+4)/((x+2)(x+3))}}}
{{{(2x+9)/((x+2)(x+3))}}}
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and you can finish that by simplifying the denominator, which you already know from the start, the LCD.