SOLUTION: If (ab)/(b - a) = 1 and a does NOT equal b, what is a in terms of b? A) (b + 1)/b B) b/(b + 1) C) (b+1)/(b-1) D) 1 - (1/b) E) b/(b-1)

Algebra ->  Expressions -> SOLUTION: If (ab)/(b - a) = 1 and a does NOT equal b, what is a in terms of b? A) (b + 1)/b B) b/(b + 1) C) (b+1)/(b-1) D) 1 - (1/b) E) b/(b-1)      Log On


   

Question 469825: If (ab)/(b - a) = 1 and a does NOT equal b, what is a in terms of b?
A) (b + 1)/b
B) b/(b + 1)
C) (b+1)/(b-1)
D) 1 - (1/b)
E) b/(b-1)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
What this problem is asking you to do is to solve for a.
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Do you recognize why the problem says that a is NOT equal to b? It's because if a = b then the denominator of (b - a) would be equal to zero, and as you know, division by zero is not permitted in algebra.
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So the problem you were given is:
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%28ab%29%2F%28b+-+a%29+=+1
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First get rid of the denominator (b - a) by multiplying both sides of the equation by (b - a) to get:
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ab+=+b+-+a
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Next add +a to both sides to get rid of the -a on the right side. When you do, the equation becomes:
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ab+%2B+a+=+b
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Factor the left side by removing a from both terms to get:
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a%28b%2B1%29+=+b
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Solve for a by dividing both sides by (b+1) and you have:
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a+=+b%2F%28b%2B1%29
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Notice that this is answer B in your list of possible answers.
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Hope this helps you to understand the problem.