Simplify and show work for the equation

Question

Simplify: . Show work

 

1/(x+2)-2/(x^2+5x+6)

 

Answer 1

1/(x + 2) - 2/(x^2+5x+6)

 

Use FOIL: x^2 + 5x + 6 = (x + 3)(x + 2)

 

1/(x + 2) - 2/((x + 3)(x + 2)))

 

multiply the first term by (x + 3)/(x + 3)

 

(x + 3)/((x + 3)(x + 2)) - 2/((x + 3)(x + 2)) = (x + 3 - 2)/((x + 3)(x + 2)) =

 

(x + 1)/((x + 3)(x + 2)) = (x + 1)/(x^2 + 5x + 6)

Answer 2

(1/ (X+2) ) -  2 / ( X^2 + 5X +6) =

 

  1/ ( X+2 ) - 2/ ( X + 2) ( X +3 ) =

 

(  X +3 ) -2  / ( X +2)( X+3 )

 

    ( X +1 ) / ( X +2 ) ( X+3)