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4 May, 11:58

X+4 divided by x^2+16

Why can't it be simplified?

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  1. 4 May, 12:19
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    Let's try to simplify x^2 + 16. It's a sum of two squares:

    x^2 + 16 = 0

    x^2 = - 16

    The problem is, we can't take a square root of a negative. This is where imaginary numbers come in.

    Remember that square roots have a plus or minus symbol outside:

    ±√-16 = ±4i

    Our two roots are 4i and - 4i. Therefore, the trinomial simplifies to:

    (x + 4i) (x - 4i)

    If we attempt to divide x + 4 by these two binomials, we will find that 4 and 4i are not like terms. Therefore, we can't simplify this expression.
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