If ab/a + b = 2, then what is a in terms of b? : Problem Solving (PS)

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

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Math Expert

Joined: 02 Sep 2009

Posts: 53066

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

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24 Jan 2019, 02:39

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15% (low)

Question Stats:

90% (01:29) correct

10% (01:01) wrong

based on 27 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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24 Jan 2019, 03:46

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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24 Jan 2019, 09:56

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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