Question

Find the difference. Express your answer in simple stop form.7s/s2 - 14s + 49 - 49/s2 – 14s + 49

Answer 1

The expression given is,

`(7s)/(s^2-14s+49)-(49)/(s^2-14s+49)`

Apply the fraction rule:

`\begin{gathered} (a)/(c)-(b)/(c)=(a-b)/(c) \\ =(7s-49)/(s^2-14s+49) \end{gathered}`

Factor 7s-49: 7(s-7)

`=(7\left(s-7\right))/(s^2-14s+49)`
`\begin{gathered} Factor: \\ s^2-14s+49=\left(s-7\right)^2 \end{gathered}`

Therefore,

`(7\left(s-7\right))/(s^2-14s+49)=(7\left(s-7\right))/(\left(s-7\right)^2)`

Apply exponent rule:

`\begin{gathered} \left(s-7\right)^2=\left(s-7\right)\left(s-7\right) \\ (7\left(s-7\right))/(\left(s-7\right)^2)=(7\left(s-7\right))/(\left(s-7\right)\left(s-7\right)) \end{gathered}`

Cancel out factor: s-7

`(7)/(s-7)`

Hence, the answer is

`(7)/(s-7)`