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Algebra

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(x^3+2x^2-4x-8)/(x^4-16)x(3x^2+8x+5)/3x^2+11x+10)

  • Algebra - ,

    factor each part
    here is the hardest part

    x^3 + 2x^2 - 4x - 8 , using grouping
    = x^2(x+2) - 4(x+2)
    = (x^2 - 4)(x+2)
    = (x+2)(x-2)(x+2) or (x-2)(x+2)^2

    so...
    (x^3+2x^2-4x-8)/(x^4-16)x(3x^2+8x+5)/3x^2+11x+10)
    = (x-2)(x+2)^2 /((x-2)(x+2)(x^2 + 4)) * (x+1)(3x+5)/((3x+5)(x+2))
    = (x+1)/(x^2 + 4) , x ≠ ±2, -5/3

    check by picking any value of x other than the restricted values

    e.g. let x = 1
    in original:
    = (-9)/(-15)*(16/24) = 2/5
    value of (x+1)/(x^2+4) = 2/5

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