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Consider the two expressions \(\frac{6x^3+9x^2+4x+7}{2x+3}\)  and \(3x^2+2+\frac1{2x+3}.\)

a) Show that the two expressions represent equal numbers when \(x = 10\)

b) Explain why these two expressions do not represent equal numbers when \(x=-\dfrac32.\)

c) Show that these two expressions represent equal numbers for all  other than \(-\dfrac32.\)

 Jan 8, 2024
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This is AoPS homework.  Do not post AoPS homework.

 Jan 8, 2024

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