Math 11 - Rational Expressions

I really don't understand how you find or identify the restrictions at all for rational expressions, can someone talk me through it? I have a math exam Monday and I'm stressed. Thanks.
Here are some examples for my textbook if needed...

1) 2x + 1 / 2x - 1
2) x-5 / x^2 + 3x + 2
3) 3x + 1 / 2x^2 + 5x + 2

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asked by M.
  1. the only restrictions are because you cannot divide by zero. So, check the denominator of any rational expression. Wherever it is zero, those values must be omitted from the domain. Otherwise, all real numbers are allowed.

    So, for #3 above, since
    2x^2+5x+2 = (2x+1)(x+2)
    the values x = -1/2 and -2 are not in the domain -- they would make the denominator zero. All other real values are allowed.

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    posted by Steve

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