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# If x > 1 and a/b = 1 - 1/x, then b/a =

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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15 Mar 2018, 22:59
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Difficulty:

15% (low)

Question Stats:

91% (00:45) correct 9% (01:44) wrong based on 47 sessions

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If $$x > 1$$ and $$\frac{a}{b} = 1 - \frac{1}{x}$$, then $$\frac{b}{a} =$$

A. x

B. x - 1

C. $$\frac{x - 1}{x}$$

D. $$\frac{x}{x - 1}$$

E. $$\frac{1}{x} - 1$$

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Posts: 55271
Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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15 Mar 2018, 23:00
Bunuel wrote:
If $$x > 1$$ and $$\frac{a}{b} = 1 - \frac{1}{x}$$, then $$\frac{b}{a} =$$

A. x

B. x - 1

C. $$\frac{x - 1}{x}$$

D. $$\frac{x}{x - 1}$$

E. $$\frac{1}{x} - 1$$

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Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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16 Mar 2018, 00:42
Bunuel wrote:
If $$x > 1$$ and $$\frac{a}{b} = 1 - \frac{1}{x}$$, then $$\frac{b}{a} =$$

A. x

B. x - 1

C. $$\frac{x - 1}{x}$$

D. $$\frac{x}{x - 1}$$

E. $$\frac{1}{x} - 1$$

a/b = (x-1)/x

i.e. b/a = x/(x-1)

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If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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16 Mar 2018, 06:18
Bunuel wrote:
If $$x > 1$$ and $$\frac{a}{b} = 1 - \frac{1}{x}$$, then $$\frac{b}{a} =$$

A. x

B. x - 1

C. $$\frac{x - 1}{x}$$

D. $$\frac{x}{x - 1}$$

E. $$\frac{1}{x} - 1$$

We are asked for the reciprocal of $$\frac{a}{b}$$.

We can take the reciprocal of RHS only if RHS expression is a single number or a single fraction.

(If fractions are added or subtracted on RHS, find the sum or difference. Then flip the resultant fraction.)
$$\frac{a}{b} = 1 - \frac{1}{x}$$

$$\frac{a}{b} = (\frac{1}{1}*\frac{x}{x}) - (\frac{1}{x}*\frac{x}{x})$$

$$\frac{a}{b} = \frac{x}{x}-\frac{1}{x}$$

$$\frac{a}{b} = \frac{(x-1)}{x}$$

$$\frac{b}{a} = \frac{x}{(x-1)}$$

Or use $$\frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}$$. From original fractions, use numbers in the denominator. Subtract first number from second number (b-a) for the new numerator. Multiply the numbers (ab) for the new denominator.
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Re: If x > 1 and a/b = 1 - 1/x, then b/a =  [#permalink]

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18 Mar 2018, 04:38
$$\frac{a}{b}$$= 1-$$\frac{1}{x}$$

$$\frac{a}{b}$$= $$\frac{x-1}{x}$$

Inverse the above equation

$$\frac{b}{a}$$=$$\frac{x}{x-1}$$

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Re: If x > 1 and a/b = 1 - 1/x, then b/a =   [#permalink] 18 Mar 2018, 04:38
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