# Conditional identity

1. Mar 13, 2014

### rama

1. The pratement, all variables and given/known data
If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d

2. Relevant equations

3. The attempt at a solution
a=1÷(1-b)
a-1÷(1-b)=0
{a(1-b)-1)}÷1-b=0
a-ab-1=0
a-ab=1
similarly
b-bc=1
c-cd=1
could any of you please give a hint, this was on test for 4 marks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 13, 2014

### pasmith

You are given
$$b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}$$
Simplify the right hand side and then use
$$a = \frac{1}{1 - b}.$$

3. Mar 13, 2014

### rama

pasmith thanks for your time I finally got it
actually I hesitated to post such easy problems (for this PF level)
good to see you taking time on helping me
by the way how do you write fractions?

4. Mar 13, 2014

For example \frac{1}{2} and putting two #s around will give $\frac{1}{2}$