Question

Divide simplify your answer

Answer 1

`\large\boxed{(2s-6)/(s+3)}`

Explanation:

`s^2-9=s^2-3^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(s-3)(s+3)\\\\s^2+6s+9=s^2+2(s)(3)+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\=(s+3)^2`

`(s^2-9)/(2s)/(s^2+6s+9)/(4s)=(s^2-9)/(2s\!\!\!\!\diagup_1)\cdot(4s)/(s^2+6s+9)\\\\=((s-3)(s+3))/(2s\!\!\!\!\!\diagup_(_1))\cdot(4s\!\!\!\!\!\diagup^(^2))/((s+3)^2)=(2(s-3)(s+3))/((s+3)(s+3))\qquad\text{cancel}\ (s+3)\\\\=(2(s-3))/(s+3)=(2s-6)/(s+3)`