Calculus

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Simplify. State the nonpermissible values.

(3t^2+3t-6/2t^2-2t-4)(4t^2+4t-24/3t^2+6t-9)

This is the way I tried solving this:

3t(t-1)6(t-1)/2t(t-1)4(t-1)*4t(t-2)12(t-2)/3t(t+1)9(t-1)

(3)(t)(t-1)(2)(3)(t-1)/(2)(t)(t-1)(2)(2)(t-1)*(2)(2)(t)(t-2)(2)(2)(3)(t-2)/(3)(t)(t-1)(3)(3)(t-1)

After cancelling out all the terms I am left with:

(2)(t-2)(t-2)/(t-1)(t-1)

^ I cant cancel anything off now. But the answer is supposed to be :

2(t+2)/t+1

^ How do I get that answer?

  • Calculus -

    (3t^2+3t-6)(4t^2+4t-24)
    ===============================
    (2t^2-2t-4)(3t^2+6t-9)

    3(t^2+t-2)(4)(t^2+t-6)
    ==============================
    2(t-2)(t+1)(3)(t+3)(t-1)

    3(t+2)(t-1)(4)(t+3)(t-2)
    ==============================
    2(t-2)(t+1)(3)(t+3)(t-1)

    (2) (t+2) / (t+1)

    2

  • Calculus -

    Thank you so much Damon :)

  • Calculus -

    You are welcome.
    By the way that is undefined if t = -1 so I suppose that might be what is meant by "non-permissible"

  • Calculus -

    Thank you and yeah nonpermissible is another word for restrictions.

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