Question

Perform the indicated operations and simplify the result. Leave the numerator and denominator in your answer in factoredform.(1-1/x)/(3+1/x)

Answer 1

Assuming that x≠0 we get that:

`(1-(1)/(x))/(3+(1)/(x))=(1-(1)/(x))/(3+(1)/(x))*(x)/(x).`

Simplifying the above result we get:

`(1-(1)/(x))/(3+(1)/(x))*(x)/(x)=((1-(1)/(x))*x)/((3+(1)/(x))*x).`

Applying the distributive property we get:

`((1-(1)/(x))*x)/((3+(1)/(x))*x)=(x-1)/(3x+1).`

Therefore:

`(1-(1)/(x))/(3+(1)/(x))=(x-1)/(3x+1).`

Answer:

`\begin{equation*} (x-1)/(3x+1). \end{equation*}`