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iiamdance Group Title

simplify the rational expression. State any restrictions on the variable. p^2 - 4p - 32/p + 4 –p + 8; p ≠ –4 p – 8; p ≠ –4 –p – 8; p ≠ –4 p + 8; p ≠ –4

  • one year ago
  • one year ago

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  1. SamuelAlden917 Group Title
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    1. fully factor everything. 2. cancel as muich as you can out 3. make sure it's fully simplified 4. look at ALL denominators you have come across, set equal to 0, and thus find restrictions. (p^2 -4p -32) / (p+4) (p-8)(p+4) / (p+4) (p+4)s cancel each other out, leaving you with (p-8) / 1 p -8 Denominators: (p+4) p+4 =0 p= -4 THEREFORE p is every real number except for -4. (n^4 -11n^2 +30) / (n^4 -7n^2 +10) (n^2 -6)(n^2-5) / (n^2-5)(n^2 -2) NOTE that (n^2-5)s cancel each other out, leaving you with (n^2 -6) / (n^2 -2) can't simplify further. DENOMINATORS: (n^2-5)(n^2-2) =0 n^2-5 =0 and n^2 -2 = 0 n^2 = 5 and n^2 = 2 n= +/- √5 and n= +/- √2 THEREFORE n is all real numbers except for +/- √2, +/- √5 (x-4)(x+4) / (x+3)(x+2) / (x+4)(x+1) / (x-4)(x+2) WHICH IS THE SAME AS: (x-4)(x+4) / (x+3)(x+2) TIMES (x-4)(x+2) / (x+4)(x+1) (x+4)s cross cancel, (x+2)s cross cancel: (x-4) / (x+3) TIMES (x-4) / (x+1) (x-4)(x-4) / (x+3)(x+1) can't simplify further, denominators: (x+3)(x+2)(x+4)(x+1) =0 x+3=0 and x+2=0 and x+4=0 and x+1=0 x= -3 and x= -2 and x= -4 and x= -1 THEREFORE x is all real numbers except for -4, -3, -2, -1

    • one year ago
  2. tcarroll010 Group Title
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    \[\frac{ (p - 8)\cancel {(p + 4)} }{ \cancel {p + 4} }\]So, the only value you cannot have is: p = -4 Answer is "b"

    • one year ago
  3. SamuelAlden917 Group Title
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    That help?

    • one year ago
  4. tcarroll010 Group Title
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    The slashes are for the cancellation. You are left with "p - 8"

    • one year ago
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