How do you write 1/(1-(1/a)) as a single rational number?

Question

(1 divided by (1 minus 1 divided by a)). A is an integer.

Answer 1

[12]
1/(1-(1/a)
=1/(1- 1/a)
=1/{(a-1)/a}
=a/(a-1)

Answer 2

1 / ( 1 - (1/ a)) = 1 / [ (a -1) / a] = a / (a - 1)

Answer 3

if A is an integer then work the denominater like this

1 - 1/A
=A/A -1/A
=1-A/A^2 = P

Now 1 / P = invert and multiply 1* P
=(1) * 1-A/A^2
=(1/1) * (1-A/A^2)

ex.
1 - 1/5
=5/5 -1/5
=4/5
Now 1/(4/5) = (1/1)*(5/4)= 5/4=rational number

Answer 4

Start with the denominator only, 1 - 1/a. That's equal to a/a - 1/a or (a-1)/a. One over that expression is the same as just inverting the expression, so you get a/(a-1).

Example: If a=4, then the expression's value is 4/3. If a = -6, then the expression's value is -6/-7 = 6/7. The expression has no value (i.e., it is indeterminate) if a=1.

Answer 5

a/(a-1)

Answer 6

1/(1-(1/a)=1/((a-1)/a)=a/(a-1)