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math check

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Simplify each rational expression.

3a(a-4)^2 over a^2(a-4) I don't understand how the answer would be 3(a-4) over a because the a-4 would cancel out???

4-y^2 over y^2-2y once I simplify I get (2-y)(2+y) over (y-2)(y+2) I don't understand how the answer is -(y+2) over y

9-r^2 over r^2-3 once I simplify i get (3-r)(3+r) over (r-3)(r+3) I don't understand how the answer is -(r+3) over r

  • math check -

    3a(a-4)^2 over a^2(a-4)

    3a(a-4)(a-4) over a*a*(a-4)
    You are correct that an (a-4) would cancel, but you are left with another one because the top had the power of two on it. In addition, 1 a would also cancel, leaving you with 3(a-4)/a

    4-y^2 over y^2-2y
    Rewrite the numerator in standard form
    -y^2+4 and then factor out a -1, leaving you with -1(y^2 - 4) which then factors into: -1(y+2)(y-2)
    Then the denominator factors into:
    y(y-2). As a result, the (y-2) factors cancel, leaving you with -1(y+2)/y

    9-r^2 over r^2-3
    (Is the denominator supposed to be r^2-3r?)
    Again, rewrite: -r^2+9 --> -1(r^2-9) --> then as -1(r+3)(r-3)
    Denominator: r(r-3)
    Cancel out the (r-3)'s and you are left with -(r+3)/r

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