# How do you simplify # (1+1/x)/(1/x)#?

##### 1 Answer

Jun 16, 2016

When a fraction is in the denominator, you can treat it as multiplying by its reciprocal.

Recall that

#1/((1/x))#

#= (1/x)^(-1)#

#= 1/(x^(-1))#

#= 1*x^1#

#= x#

So if you had been multiplying by

#color(blue)((1+1/x)/(1/x))#

#= (1+1/x)*1/(1/x)#

#= (1+1/x)*(1/x)^(-1)#

#= (1+1/x)*x#

#= 1*x+1/cancel(x)*cancel(x)#

#= color(blue)(x+1)#