x/x^2+3x+2 - 1/x^2+x =?
回答 (4)
2009-02-12 10:20 am
✔ 最佳答案
x/(x^2 + 3x + 2) - 1/(x^2 + x)= x/(x^2 + 2x + x + 2) - 1/[x(x + 1)]
= x/[(x + 2)(x + 1)] - 1/[x(x + 1)]
= [x(x)]/[x(x + 2)(x + 1)] - [1(x + 2)]/[x(x + 2)(x + 1)]
= x^2/[x(x + 2)(x + 1)] - [x + 2]/[x(x + 2)(x + 1)]
= [x^2 - x - 2]/[x(x + 2)(x + 1)]
= [x^2 + x - 2x - 2]/[x(x + 2)(x + 1)]
= [(x + 1)(x - 2)]/[x(x + 2)(x + 1)]
= (x - 2)/[x(x + 1)]
2009-02-12 11:38 am
You have presented question incorrectly.
It SHOULD read as :-
x / (x² + 3x + 2) - 1 / (x² + x)
x / (x + 2)(x + 1) - 1 / x (x + 1)
x² - (x + 2)
------------------
(x + 2)(x + 1) (x)
x² - x - 2
------------------------
(x + 2)(x + 1) (x)
(x - 2)(x + 1)
---------------------------
(x + 2)(x + 1) (x)
(x - 2)
----------------
x (x + 2)
It SHOULD read as :-
x / (x² + 3x + 2) - 1 / (x² + x)
x / (x + 2)(x + 1) - 1 / x (x + 1)
x² - (x + 2)
------------------
(x + 2)(x + 1) (x)
x² - x - 2
------------------------
(x + 2)(x + 1) (x)
(x - 2)(x + 1)
---------------------------
(x + 2)(x + 1) (x)
(x - 2)
----------------
x (x + 2)
2009-02-12 9:03 am
x/[ (x + 2)/x + 1) ] - 1[/ x(x + 1) ]
Multiply with LCD : x( x + 2)(x + 1)
x mustn be -2, -1 or 0
x^2 - (x+2)
x^2 -x -2
(x+1)(x-2)
Multiply with LCD : x( x + 2)(x + 1)
x mustn be -2, -1 or 0
x^2 - (x+2)
x^2 -x -2
(x+1)(x-2)
2009-02-12 8:55 am
6
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