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hi!
i´ve got this problem i cant solve
( (4x-x^2)/(9-x^2 ) ) / ( (8-4x)/(3+x) )
thanx for your help!
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hi yaz pman!
hmm... where have all the admins/mods gone to??.
[(4x - x²)/(9 - x²)]/[(8 - 4x)/(3+x)] use the property: (a/b) / (c/d) = (a/b)(d/c)
(4x - x²)(3 + x)
------------------- expand (9 - x²) ---> (3 - x)(3 + x)
(9 - x²)(8 - 4x)
(4x - x²)(3 + x)
------------------------ (3+x) cancels out
(3 - x)(3 + x)(8 - 4x)
(4x - x²)
----------------- multiply: (3 - x)(8 - 4x) to get: (24 - 20x + 4x²)
(3 - x)(8 - 4x)
(4x - x²)
------------------- factor out a 4 in the denominator: (24 - 20x + 4x²) ----> 4(x² - 5x +6)
(24 - 20x + 4x²)
(4x - x²)
----------------- x² - 5x +6 ---> (x - 2)(x - 3)
4(x² - 5x +6)
(4x - x²)
---------------- in the numerator, complete the square of (4x - x²) to get: -(x - 2)² + 4
4(x - 2)(x - 3)
-(x - 2)² + 4 -(x - 2)² 4 -(x - 2) 1
------------------ = ------------ ----- + ------------------ = ------------- + ---------------
4(x - 2)(x - 3) 4(x - 2)(x - 3) 4(x - 2)(x - 3) 4(x - 3) (x - 2)(x - 3)
Last edited by Flowers4Carlos (2005-11-04 15:01:17)
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