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# If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

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12 Nov 2018, 01:22
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Difficulty:

15% (low)

Question Stats:

86% (00:56) correct 14% (01:36) wrong based on 53 sessions

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If $$\frac{1}{1 + \frac{1}{y - 1}} = \frac{3}{4}$$ and y ≠ 1, then y =

A. 4
B. 3
C. 2
D. 4/3
E. 1/3

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Senior Manager
Joined: 15 Feb 2018
Posts: 365
If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

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13 Nov 2018, 13:51
1
First, want to clean up the denominator.

$$\frac{1}{{{(y-1)/(y-1)}+{1/(y-1)}}}$$

$$\frac{1}{{(y-1+1)/y-1}}$$

$$\frac{1}{{y/y-1}}$$

$$\frac{1}{1}÷\frac{y}{(y-1)}$$

$$\frac{1}{1}·\frac{(y-1)}{y}$$

$$\frac{y-1}{y}=\frac{3}{4}$$

Use cross multiplication
4(y-1)=3y
4y-4=3y
y-4=0
y=4

A

And for those that got distracted by y≠1, that is simply so the denominator y-1 doesn't become 1-1=0 as 0 cannot be the denominator.
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Re: If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =  [#permalink]

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27 Jan 2019, 20:29
Bunuel wrote:
If $$\frac{1}{1 + \frac{1}{y - 1}} = \frac{3}{4}$$ and y ≠ 1, then y =

A. 4
B. 3
C. 2
D. 4/3
E. 1/3

Multiplying the left side by (y-1)/(y-1), we have:

(y - 1)/[(y - 1) + 1] = 3/4

4y - 4 = 3y - 3 + 3

y = 4

Alternate solution:

We can cross multiply and obtain:

4 = 3 + 3/(y - 1)

1 = 3/(y - 1)

y - 1 = 3

y = 4

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Re: If 1/(1 + 1/(y - 1)) = 3/4 and y ≠ 1, then y =   [#permalink] 27 Jan 2019, 20:29
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