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angelina202
@angelina202
August 2022
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Помогите упростить выражение, пожалуйста.
y^2-4/2-9y *( y+2/y ^2+y-6 - y-3/y 2+5y+6)
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svetazuna
(у²-4)/(2-9у) * ((у+2)/(у²+у-6) - (у-3)/(у²+5у+6)) =
= (у²-4)/(2-9у) * ((у+2)/(у+3)(у-2) - (у-3)/(у+2)(у+3)) =
= (у²-4)/(2-9у) * ((у+2)(у+2)/(у+3)(у-2)(у+2) - (у-3)(у-2)/(у+3)(у-2)(у+2)) =
= (у²-4)/(2-9у) * ((у²+4у+4)/(у+3)(у-2)(у+2) - (у²-5у+6)/(у+3)(у-2)(у+2))=
= (у²-4)/(2-9у) * ((у²+4у+4 - у²+5у-6)/(у+3)(у-2)(у+2)) =
= (у²-4)/(2-9у) * ((9у-2)/(у+3)(у-2)(у+2)) =
= -(у²-4)(9у-2) * (9у-2)/(у+3)(у²-4) =
= -1/(у+3)
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Answers & Comments
= (у²-4)/(2-9у) * ((у+2)/(у+3)(у-2) - (у-3)/(у+2)(у+3)) =
= (у²-4)/(2-9у) * ((у+2)(у+2)/(у+3)(у-2)(у+2) - (у-3)(у-2)/(у+3)(у-2)(у+2)) =
= (у²-4)/(2-9у) * ((у²+4у+4)/(у+3)(у-2)(у+2) - (у²-5у+6)/(у+3)(у-2)(у+2))=
= (у²-4)/(2-9у) * ((у²+4у+4 - у²+5у-6)/(у+3)(у-2)(у+2)) =
= (у²-4)/(2-9у) * ((9у-2)/(у+3)(у-2)(у+2)) =
= -(у²-4)(9у-2) * (9у-2)/(у+3)(у²-4) =
= -1/(у+3)