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Simplify each expression.
1. 2x+8/x^2-16
2. 1+x/x^2+x
3. x^2-12x-28/x^2-14x
4. x^2+7x+10/x^2-4

  • Math -

    You probably meant
    1. (2x+8)/(x^2-16)

    then this factors to
    = 2/(x-4), where x is not equal to -4

    With the proper use of brackets, the others factor as well.

    Let me know how you made out with them.

  • Math -

    Thank you so much.

    1. (x^2-12x-28)/(x^2-14x)
    Answer: (x+2)/(x)
    2. (x^2+7x+10)/(x^2-4)
    Answer: (x+5)/(x-2)
    3. (y^2-16)/(y^2-7y+12)
    Answer: (y+4)/(y-3)

    Could you check my answers for these questions. I will really appeciate it. Thank you so much again.

  • Math -

    Your answers are all correct.

    Have you learned about restrictions?
    e.g. in the first one you probably had
    (x-14)(x+2)/[(x(x-14)] , then canceled the x-14.
    but suppose x = 14. Didn't you just divide by zero ?

    That is why we have to exclude the value of the variable which would have made that denominator zero.
    so the complete answer to that one would have been ...
    (x+2)/x , x not equal to 14

  • Math -

    No, I haven't. Thank you so much.

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