Question

Find the quotient and simplify​

Answer 1

Answer:

$\large\boxed{\dfrac{9}{s^2-5s}}$

Step-by-step explanation:

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