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Liviammello
@Liviammello
April 2020
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Escreva na forma mais simples a seguinte expressão: a/(a-b)(a-c) + b/(b-c)(a-b) + (c/(a-c)(b-c)
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3478elc
Verified answer
a + b + c
(a-b)(a-c) (b-c)(a-b) (a-c)(b-c)
a(b-c) + b(a-c) + c(a-b)
(a-b)(a-c)(b-c)
ab - ac + ab - bc + ac - bc
(a-b)(a-c)(b-c)
ab + ab - bc - bc
(a-b)(a-c)(b-c)
2ab - 2bc
(a-b)(a-c)(b-c)
2b(a -c )
(a-b)(a-c)(b-c)
2b
(a-b)(b-c)
11 votes
Thanks 17
laurelidb
a/(a-b)(a-c) + b/(b-c)(a-b) + (c/(a-c)(b-c)
MMc= (a-b) (a-c) (b-c)
a( b-c) + b(a-b) + c(a-b)
(a-b) (a-c) (b-c)
=
ab-ac +ab-b² +ac -cb
(a-b) (a-c) (b-c)
=
ab-ac +ab-b² +ac -cb
ab²-abc-ab² + b²c-bc²
= 2
ab -b² -cb
-abc + b²c -bc²
=b (2a -b -c )
b ( -ac +bc - c²)
=
2a - b - c
-ac + bc - c
3 votes
Thanks 3
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Verified answer
a + b + c(a-b)(a-c) (b-c)(a-b) (a-c)(b-c)
a(b-c) + b(a-c) + c(a-b)
(a-b)(a-c)(b-c)
ab - ac + ab - bc + ac - bc
(a-b)(a-c)(b-c)
ab + ab - bc - bc
(a-b)(a-c)(b-c)
2ab - 2bc
(a-b)(a-c)(b-c)
2b(a -c )
(a-b)(a-c)(b-c)
2b
(a-b)(b-c)
MMc= (a-b) (a-c) (b-c)
a( b-c) + b(a-b) + c(a-b)
(a-b) (a-c) (b-c)
= ab-ac +ab-b² +ac -cb
(a-b) (a-c) (b-c)
=ab-ac +ab-b² +ac -cb
ab²-abc-ab² + b²c-bc²
= 2ab -b² -cb
-abc + b²c -bc²
=b (2a -b -c )
b ( -ac +bc - c²)
= 2a - b - c
-ac + bc - c