Question 116168
{{{5/(x+6)+2/(x^2+7x+6)=3/(x+1)}}} Start with the given expression



{{{5/(x+6)+2/((x+1)(x+6))=3/(x+1)}}} Factor 



{{{((x+6)(x+1))(5/(x+6)+2/((x+1)(x+6)))=((x+6)(x+1))(3/(x+1))}}} Multiply both sides by the LCD {{{(x+6)(x+1)}}}




{{{5(x+1)+2=3(x+6)}}} Distribute



{{{5x+5+2=3x+18}}} Distribute again



{{{5x+7=3x+18}}} Combine like terms on the left side



{{{5x=3x+18-7}}}Subtract 7 from both sides



{{{5x-3x=18-7}}} Subtract 3x from both sides



{{{2x=18-7}}} Combine like terms on the left side



{{{2x=11}}} Combine like terms on the right side



{{{x=(11)/(2)}}} Divide both sides by 2 to isolate x



--------------------------------------------------------------

Answer:

So our answer is {{{x=11/2}}}  (which is approximately {{{x=5.5}}} in decimal form)