what is (a=1-frac{1}{b}) and (b=1-frac{1}{c}), find the value of (c-frac{1}{a})

Question: what is (a=1-frac{1}{b}) and (b=1-frac{1}{c}), find the value of (c-frac{1}{a})
- Keywords:
  algebra,
  equation,
  fraction
Asked by cope534harm62 to tomranner, margaretduff, Laura B, janmckendrick, Daniel on 22 Dec 2025.
- Margaret Duff answered on 22 Dec 2025:
  
  I got (c-frac{1}{a}) =1 by rearranging (b=1-frac{1}{c}) to get a value for c ( assuming b is not equal to 1) and then (assuming a not equal to zero) subbing in the value for c and a into (c-frac{1}{a}) and rearranging.
  
  Can we ask where the question came from/why you are interested in it?

Question: what is (a=1-frac{1}{b}) and (b=1-frac{1}{c}), find the value of (c-frac{1}{a})