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If ab/a + b = 2, then what is a in terms of b?

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If ab/a + b = 2, then what is a in terms of b?  [#permalink]

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New post 24 Jan 2019, 03:39
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:20) correct 14% (01:28) wrong based on 34 sessions

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If \(\frac{ab}{a + b} = 2\), then what is a in terms of b?


A \(\frac{b – 2}{2b}\)

B \(\frac{2b}{b + 2}\)

C \(\frac{2b}{b – 2}\)

D \(\frac{b}{2b – 2}\)

E \(\frac{b + 2}{2b}\)
Spoiler: OA

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Re: If ab/a + b = 2, then what is a in terms of b?  [#permalink]

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New post 24 Jan 2019, 04:46
Bunuel wrote:
If \(\frac{ab}{a + b} = 2\), then what is a in terms of b?


A \(\frac{b – 2}{2b}\)

B \(\frac{2b}{b + 2}\)

C \(\frac{2b}{b – 2}\)

D \(\frac{b}{2b – 2}\)

E \(\frac{b + 2}{2b}\)


solve the expression
we would ge
ab=2a+2b
a= 2b / (b-2)
IMO C
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Re: If ab/a + b = 2, then what is a in terms of b?  [#permalink]

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New post 24 Jan 2019, 10:56
1
lets solve in a different manner
given
\(ab/(a+b)=2\)
lets reverse.
\((a+b)/ab= 1/2\)
thus \(1/a+1/b= 1/2\)
\(1/a= 1/2-1/b\)
\(1/a = (b-2)/2b\)
reverse again:
\(a= 2b/(b-2)\)
there for C
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Re: If ab/a + b = 2, then what is a in terms of b?  [#permalink]

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New post 24 Jan 2019, 22:18
\(\frac{ab}{(a+b)}=2\)
\(ab=2(a+b)\)
\(ab=2a+2b\)
\(ab-2a=2b\)
\(a(b-2)=2b\)
\(a=\frac{2b}{(b-2)}\)

Hence, the answer is C.
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Re: If ab/a + b = 2, then what is a in terms of b?   [#permalink] 24 Jan 2019, 22:18
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