- If a, b, and c are numbers such that a/b=3, b/c=7, then a+b/b+c is equal to what?
Please answer this question in a detailed way if you can, and also please provide me with the basic concept this problem originated from.
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Answer by John
a/b=3 49/7=7 for the reason of 7*7
147/49=3 for the reason of 49*3
- Show that (a, b – ta) = (a, b).
where (a,b) is the greatest common divisor of a and b and a and b do not equal 0
Answer by kb
Let d = (a, b) and e = (a, b – ta).
(i) Since d = (a, b), we have d | a and d | b.
Thus, d | (-ta) and so d | (b – ta).
Since d | a and d|(b – ta), we have that e | d.
(ii) Since e = (a, b – ta), we have e | a and e | (b – ta).
So, e | ta ==> e | (ta + (b – ta)) = b.
Since e | a and e | b, we have that d | e.
By (i) and (ii), we conclude that d = e (since the gcd is positive).
I hope this helps!