Simplify

[Lionheart3239]

1/((1/x)+1) =
1/((x+1)/x) =
x/(x+1)

Please someone explain how to get from step 1 to step 2, i understand the x goes on top in step 3.

[tommywallach]

They're rewriting the 1 in the denominator (the "+1" part) as x/x. This gives it a common denominator with the 1/x part, and then we can just add the numerators.

-t

P.S. I always encourage my students not to say things like "the x goes up top." This kind of thinking confuses arithmetic. Always think in terms of multiplication, division, addition, and subtraction. I don't even like the term "cancel," which muddies the clarity of the operation.

[Lionheart3239]

Thank you for your explanation and reply back.

[tommywallach]

No problem!