Simplify the following \frac{ (1)/(x) + 1 } { \frac {1}{x} }

Question

Simplify the following
`\frac{ (1)/(x) + 1 } { \frac {1}{x} }`

Answer 1

Good evening, Riley!

Used properties:


`\star~\boxed{\mathsf{a = (ax)/(x), \ \ x\\eq 0}}\\ \\ \\ \star~\boxed{\mathsf{((a)/(b))/((c)/(d)) = (ad)/(bc)}}`

Now, note that:


`\mathsf{1 = (x)/(x),\ x\\eq 0}`

So:


`\mathsf{(\frac 1 x + \frac x x )/(\frac 1 x) = ((x+1)/(x))/(\frac 1 x)}=} \mathsf{(x)/(1)(x+1)/(x) = \boxed{x + 1}}`