Question

Simplify the following 0%7B1%7D%7Bx%7D%20%7D" id="TexFormula1" title="\frac{ \frac{1}{x} + 1 } { \frac {1}{x} }" alt="\frac{ \frac{1}{x} + 1 } { \frac {1}{x} }" align="absmiddle" class="latex-formula">

Answer 1

Good evening, Riley!

Used properties:

$\star~\boxed{\mathsf{a = \dfrac{ax}{x}, \ \ x\neq 0}}\\ \\ \\ \star~\boxed{\mathsf{\dfrac{\frac{a}{b}}{\frac{c}{d}} = \dfrac{ad}{bc}}}$

Now, note that:

$\mathsf{1 = \dfrac{x}{x},\ x\neq 0}$

So:

$\mathsf{\dfrac{\frac 1 x + \frac x x }{\frac 1 x} = \dfrac{\frac{x+1}{x}}{\frac 1 x}}=} \mathsf{\dfrac{x}{1}\dfrac{x+1}{x} = \boxed{x + 1}}$