Question

Simplify the following complex rational expression completely. Detailed Step By Step

Answer 1

Answer:
`((1)/(7)+(1)/(x))/((x)/(7)-(7)/(x))=(1)/(x-7)`

Step-by-step explanation:

Given:

`((1)/(7)+(1)/(x))/((x)/(7)-(7)/(x))`

Let us write the numerator as a single fraction, as well as the denominator. This can be written as:

`((x+7)/(7x))/((x^2-49)/(7x))`

Division by a fraction may become a mu

`\begin{gathered} (x+7)/(7x)*(7x)/(x^2-49) \\ \\ =(x+7)/(7x)*(7x)/((x+7)(x-7)) \\ \\ =(1)/(x-7) \end{gathered}`