Question

Do division:
(x^2 - y^2+6x+9): (x+y+3)

Answer 1

Rearrange the terms and you'll get
{(x^2 +6x+9)-( y^2)}: (x+y+3)
= {(x^2 +3x+3x +9)-(y^2)} : (x+y+3)
= [{x (x+3) + 3 (x+3)} -(y^2)]: (x+y+3)
= { (x+3)(x+3) - (y^2)} : (x+y+3)
= { (x+3)^2 -y^2 } :(x+y+3)

Apply the identity a^2 -b^2 = (a+b)(a-b)

= ( x+3+y)(x+3-y) : (x+y+3)
= (x +y +3)(x-y+3): (x+y+3)
= (x-y+3)