Question

Find the quotient and simplify​

Answer 1

`\large\boxed{(9)/(s^2-5s)}`

Explanation:

`(s+5)/(s^2)/(s^2-25)/(9s)=(s+5)/(s\!\!\!\!\diagup_s^2)\cdot(9s\!\!\!\!\diagup^1)/(s^2-5^2)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(s+5)/(s)\cdot(9)/((s-5)(s+5))\\\\\text{cancel}\ (s+5)\\\\=(1)/(s)\cdot(9)/(s-5)=((1)(9))/(s(s-5))\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=(9)/((s)(s)+(s)(5))=(9)/(s^2-5s)`