How do I simplify r+4/r^2-1 × r^2-16/r+1?

That × in the middle is a multiplication sign. And the "r" is the variable.

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  • 6 years ago
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    r+4/r^2-1 × r^2-16/r+1 = (r^3 + 4 - r^2)/r^2 x (r^3 - 16 + r)/r

    = 1/r^3 x (r^3 + 4 - r^2) x (r^3 - 16 + r)

    = 1/r^3 x [r^3 x (r^3 - 16 +r) + 4 x (r^3 - 16 +r) - r^2 x (r^3 - 16 +r)]

    = 1/r^3 x (r^6 - 16r^3 + r^4 + 4r^3 - 64 +4r - r^5 +16r^2 - r^3)

    = 1/r^3 x (r^6 -r^5 + r^4 - 13r^3 +16r^2 +4r -64)

    = r^3 - r^2 + r -13 +16/r + 4r^2 - 64/r^3

    Therefore r^3 - r^2 + r -13 +16/r + 4r^2 - 64/r^3 is the final simplified answer

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