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# Quant

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Intern
Joined: 10 Apr 2016
Posts: 2

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30 Aug 2018, 02:52

Question: (a+b)/(a-b)+(a-b)/(a+b)=5.1/5

Kindly provide each and every step with explanation

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Joined: 02 Sep 2009
Posts: 52902

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30 Aug 2018, 03:29
Purushottam wrote:

Question: (a+b)/(a-b)+(a-b)/(a+b)=5.1/5

Kindly provide each and every step with explanation

Posted from my mobile device

It should be $$5\frac{1}{5}$$, not $$\frac{5.1}{5}$$ for a/b to be 3/2.

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

$$\frac{(a+b)(a+b)}{(a-b)(a+b)}+\frac{(a-b)(a-b)}{(a-b)(a+b)}= \frac{26}{5}$$;

$$\frac{(a+b)(a+b)+(a-b)(a-b)}{(a-b)(a+b)}=\frac{26}{5}$$;

$$\frac{(a^2+2ab+b^2)+(a^2-2ab+b^2)}{a^2-b^2}=\frac{26}{5}$$;

$$\frac{2(a^2+b^2)}{a^2-b^2}=\frac{26}{5}$$;

$$10(a^2+b^2)=26(a^2-b^2)$$;

$$10a^2+10b^2=26a^2-26b^2$$;

$$36b^2=16a^2$$;

$$\frac{a^2}{b^2}=\frac{36}{16}$$;

$$\frac{a^2}{b^2}=\frac{9}{4}$$;

$$\frac{a}{b}=\frac{3}{2}$$ or $$\frac{a}{b}=-\frac{3}{2}$$.

Hope it's clear.
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Intern
Joined: 10 Apr 2016
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04 Sep 2018, 00:51
Thank you and yeah the problem itself is wrongly structured by the question setter hence I could not realise it that time

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Intern
Joined: 20 Aug 2018
Posts: 6
Location: United States (NJ)
Concentration: Finance, Economics
GPA: 3.5
WE: Engineering (Energy and Utilities)

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04 Sep 2018, 11:26

Question: (a+b)/(a-b)+(a-b)/(a+b)=5.1/5

((a+b)(a+b)+(a-b)(a-b))(a-b)(a+b)

(a^2+2ab+b^2+a^2-2ab+b^2)/a^2-b^2

(2a^2+2b^2)/(a^2-b^2)

2(a^2+b^2)/(a^2-b^2)=5.1/5

10(a^2+b^2)=5.1(a^2-b^2)
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Joined: 02 Sep 2009
Posts: 52902

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04 Sep 2018, 20:20
Dlc930 wrote:

Question: (a+b)/(a-b)+(a-b)/(a+b)=5.1/5

((a+b)(a+b)+(a-b)(a-b))(a-b)(a+b)

(a^2+2ab+b^2+a^2-2ab+b^2)/a^2-b^2

(2a^2+2b^2)/(a^2-b^2)

2(a^2+b^2)/(a^2-b^2)=5.1/5

10(a^2+b^2)=5.1(a^2-b^2)

Check here: https://gmatclub.com/forum/quant-274711.html#p2121895
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Re: Quant   [#permalink] 04 Sep 2018, 20:20
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