упростите выражение x^2-4x/x-3 (x/x-4 + 8/x^2-3x-4 + 2/x+1). Created by MsPi. algebra-ru

x+1)...

July 2022 1 11 Report

упростите выражение
x^2-4x/x-3 (x/x-4 + 8/x^2-3x-4 + 2/x+1)

Answers & Comments

m11m х²-4х * ( х + 8 + 2 ) = х²-4х * ( х + 8 + 2 ) =
х-3 ( х-4 х²-3х-4 х+1 ) х-3 ( х-4 (х+1)(х-4) х+1 )

Разложим х²-3х-4 на множители:
х²-3х-4=0
Д=9+4*4=25
х₁=3-5=-1
2
х₂=3+5=4
2
х²-3х-4=(х+1)(х-4)

=х²-4х * (х(х+1)+8+2(х-4)) = х²-4х * х²+х+8+2х-8 = х(х-4) * х²+3х =
х-3 ( (х+1)(х-4) ) х-3 (х+1)(х-4) х-3 (х+1)(х-4)

=х * (х²+3х) = х²(х+3)
(х-3)(х+1) (х-3)(х+1)

11 votes Thanks 15

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