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

1 Answer
Truong-Son N.
Jun 16, 2016

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

Recall that #1/u = u^(-1)#. In that case, if we let #u = 1/x#, then:

#1/((1/x))#

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

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

#= 1*x^1#

#= x#

So if you had been multiplying by #1/(1/x)#, you could instead multiply by #x# to accomplish the same thing.

#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)#

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