What is (1/x)/1-1/x

Question

I am getting ready for a quiz, but I can't remember how to simplify this.

Answer 1

I assume you are asking about (1/x) divided by (1-1/x).

 

Due to the fact the answering system does not use fancy formatting of fractions, you may want to write things down on a piece of paper for clarity as I show it to you.

 

First, you have a compound fraction. There are fractions in the numerator and fractions in the denominator. The first thing you want to do, is get rid of the compound fractions. Start with the denominator.

 

The denominator is 1-1/x. This can be simplified by expressing 1 with a denominator of x, namely x/x. Then, simplify.

 

x/x - 1/x = (x-1)/x.

 

Now, we have (1/x) in the numerator, and (x-1)/x in the denominator.

 

When you have a fraction divided by another fraction, you can multiply the top fraction by the inverse of the bottom fraction. This is because multiplication and division are inverses of each other.

 

Flip the denominator and multiply it by the numerator:

 

[1/x] * [x/(x-1)]

 

Now, the X on the bottom of the first fraction can cancel with the x on the top of the second fraction, yielding:

 

1 / (x-1)

 

It was a pleasure helping you out. If you need any clarity on this topic, or need future help, please feel free to contact me.