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

Answer 1

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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Answer 2

To simplify the expression (1+1/x)/(1/x), we can follow these steps:

  1. Start by simplifying the denominator (1/x) by taking its reciprocal, which gives us x/1 or simply x.

  2. Now, we can rewrite the expression as (1+1/x) * (x/1).

  3. Next, we can simplify the numerator (1+1/x) by finding a common denominator. The common denominator is x, so we rewrite 1 as x/x and get (x/x + 1/x).

  4. Combining the terms in the numerator, we have (x+1)/x.

  5. Finally, we multiply the numerator (x+1) by the denominator x, giving us (x+1)*x.

Therefore, the simplified expression is (x+1)*x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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