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# If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))

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Joined: 02 Sep 2009
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If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))  [#permalink]

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23 Jun 2020, 03:05
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35% (medium)

Question Stats:

72% (02:19) correct 28% (02:57) wrong based on 32 sessions

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If $$\frac{a}{b}=\frac{3}{5}$$, then what is the value $$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$?

A. 9/100
B. 1
C. 100/9
D. 50/9
E. 25/9

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Re: If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))  [#permalink]

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23 Jun 2020, 03:14
1
a/b = 3/5
=> a = 3b/5

Numerator = b(a+b)(b/a - 1)
Numerator = b (3b/5 + b) (5/3 - 1)
Numerator = b^2 * (8/5) * (2/3)

Denominator = a(a-b)(a/b - 1)
Denominator = (3b/5) (-2b/5) (-2/5)
Denominator = b^2 * (3/5) * (4/25)

=> N / D = (16/15) / (12/125)
=> N / D = 100/9

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Re: If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))  [#permalink]

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23 Jun 2020, 03:44
Bunuel wrote:
If $$\frac{a}{b}=\frac{3}{5}$$, then what is the value $$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$?

A. 9/100
B. 1
C. 100/9
D. 50/9
E. 25/9

Substitute a = 3 and b = 5 in $$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$

$$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$ = $$\frac{5(3+5)(\frac{5}{3}-1)}{3(3-5)(\frac{3}{5 }-1)}$$

$$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$ = $$\frac{40*(2}{3)/(-6)*(-2/5)}$$ = $$\frac{40*2*5}{3*6*2} = \frac{100}{9}$$

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Re: If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))  [#permalink]

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02 Jul 2020, 12:21
a/b = 3/5
a = 3b/5

b(a+b)(b/a - 1)
=b (3b/5 + b) (5/3 - 1)
= b^2 * (8/5) * (2/3)

a(a-b)(a/b - 1)
= (3b/5) (-2b/5) (-2/5)
= b^2 * (3/5) * (4/25)

b(a+b)(b/a - 1) / a(a-b)(a/b - 1) = (b^2 * (8/5) * (2/3)) / (b^2 * (3/5) * (4/25))
=100/9
Re: If a/b = 3/5, then what is the value b(a + b)(b/a - 1)/(a(a - b)(a/b))   [#permalink] 02 Jul 2020, 12:21