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AngelOfDarkness123
@AngelOfDarkness123
July 2022
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Сократить дроби(40 баллов):
1) [tex] \frac{7a^2+14a+14}{(a+1)^4-1} [/tex]
2) [tex] \frac{a^2-9}{a^2-4a+3} [/tex]
3) [tex] \frac{3+5a-2a^2}{a^2-9} [/tex]
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MizoriesKun
1) 7а²+14а+14 =7(а²+2а+2)
а²+2а+2=(х+1)²
7а²+14а+14 7(а²+2а+2) 7(а²+2а+2) 7(а²+2а+2)
----------------------- = -------------- = -----------------------------= ----------------------- =
(х+1)
⁴-1 (х+1)⁴-1 ( (х+1)²-1 )( (х+1)²+1 ) (х²+2х)(х²+2х+2)
7 7
= ----------------- = ---------------
(х²+2х) х*(х+2)
------------------------------------------------------------------------------------------------------
а
²-9 (а-3)(а+3) а+3
-------- = ---------------------- = ---------
а
²-4а+3 (а-3)(а-1) а-1
---------------------------------------------------------------------------------------------------
3+5а-2а
² -2(а+0.5)(а -3) (-2а-1)(а-3) -2х-1
------------ =--------------------- = -------------------- = ------------
а
²-9 (а-3)(а+3) (а-3)(а+3) а+3
-2а
²+5а+3=0
25+24=49
-5+7/-4= -1/2=-0,5
-5-7/-4= 3
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Answers & Comments
а²+2а+2=(х+1)²
7а²+14а+14 7(а²+2а+2) 7(а²+2а+2) 7(а²+2а+2)
----------------------- = -------------- = -----------------------------= ----------------------- =
(х+1)⁴-1 (х+1)⁴-1 ( (х+1)²-1 )( (х+1)²+1 ) (х²+2х)(х²+2х+2)
7 7
= ----------------- = ---------------
(х²+2х) х*(х+2)
------------------------------------------------------------------------------------------------------
а²-9 (а-3)(а+3) а+3
-------- = ---------------------- = ---------
а²-4а+3 (а-3)(а-1) а-1
---------------------------------------------------------------------------------------------------
3+5а-2а² -2(а+0.5)(а -3) (-2а-1)(а-3) -2х-1
------------ =--------------------- = -------------------- = ------------
а²-9 (а-3)(а+3) (а-3)(а+3) а+3
-2а²+5а+3=0
25+24=49
-5+7/-4= -1/2=-0,5
-5-7/-4= 3