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23 February, 11:49

Which expression is equivalent to x^2+3x+3+[ (2x^2+13x+15) / (x+5) ]?

A) x^2+9x+9

B) x^2+5x+6

C) x^2+9x+48

D) x^2+5x+19

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  1. 23 February, 13:17
    0
    B). x^2 + 5x + 6.

    Step-by-step explanation:

    x^2 + 3x+3 + [ (2x^2 + 13x + 15) / (x + 5) ]

    = x^2 + 3x+3 + [ (2x^2 + 10x + 3x + 15) / (x + 5) ]

    = x^2 + 3x+3 + [ (2x (x + 5) + 3 (x + 5) / (x + 5) ]

    = x^2 + 3x+3 + [ (2x + 3) (x + 5) / (x + 5) ]

    = x^2 + 3x + 3 + (2x + 3)

    = x^2 + 5x + 6.
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