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Source: — Problem Solving |

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by Anurag@Gurome » Tue Aug 23, 2011 8:36 pm
marmar29 wrote:wht is the simplest form of ths (10 a^2- 15 a b)/(4a^2- 9 b^2 )
(10a²- 15ab) = 5a(2a - 3b)
(4a² - 9b²) = (2a - 3b)(2a + 3b)

Hence, (10a²- 15ab)(4a² - 9b²) = 5a(2a - 3b)/[(2a - 3b)(2a + 3b)]
If 2a is not equal to 3b then, (10a²- 15ab)(4a² - 9b²) = 5a/(2a + 3b)

The best answer is C.
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by GmatKiss » Wed Aug 24, 2011 4:11 am
(10 a^2- 15 a b)/(4a^2- 9 b^2 )

= 5a(2a-3b)/(2a+3b)(2a-3b) - Formula: (a^2-b^2)= (a+b)(a-b)
= 5a/(2a+b) -> C

[spoiler]IMO:C[/spoiler]
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by gmatdriller » Wed Aug 24, 2011 8:58 am
I doubt whether this problem requires the stress of any algebraic simplification.
Since the options are in the lowest form of the original expression, we expect that
both have the same value if "a" and "b" are given some values.

Let a=b=1.
The original expression reduces to 1.
From the options given, only choice C equates to 1.
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