Incorrect in solving a/b−a/c=1 for c

iescabroussexg 2022-09-11 Answered
Incorrect in solving a b a c = 1 for c
I have this:
a b a c = 1
Solve for c. Then,
a b a c = 1 b c
= a c a b = b c
= a ( c b ) = b c
c = b c a + b
This is my final result.
But the correct result is:
c = a b a b
What I development wrong in this equation ?
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Answers (2)

Andrejkoxg
Answered 2022-09-12 Author has 20 answers
To isolate c we can proceed as follow
a b a c = 1 a c = a b 1 = a b b c a = b a b c = a b a b

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Paul Reilly
Answered 2022-09-13 Author has 1 answers
You have expressed the solution to c in terms of c, where you need to have it in terms of a and b. This is what gives you a different(although correct) answer.
From a c a b = b c, you should have taken the variables with c to one side, like so:
a c b c = a b c ( a b ) = a b
Can you continue from here?

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