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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: 58335
If ab/a + b = 2, then what is a in terms of b?  [#permalink]

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24 Jan 2019, 03:39
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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 $$\frac{b + 2}{2b}$$

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

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