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## #1 2005-11-05 13:22:49

pman
Member

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### really need help!!!

hi!
i´ve got this problem i cant solve

#### Code:

` ( (4x-x^2)/(9-x^2 ) ) /  ( (8-4x)/(3+x) )`

## #2 2005-11-05 14:00:37

Flowers4Carlos
Full Member

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### Re: really need help!!!

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 (2005-11-05 14:01:17)