anonymous
  • anonymous
Simplify completely quantity 8 x minus 16 over quantity x squared minus 13 x plus 22 and find the restrictions on the variable.
Mathematics
jamiebookeater
  • jamiebookeater
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
\[\huge\frac{8x-16}{x^2-13x+22}\]?
anonymous
  • anonymous
I got x-5/x+1 as my answer but I don't know what the restriction would be

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misty1212
  • misty1212
did you factor the denomiantor?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Sorry I meant 8/x-11
misty1212
  • misty1212
\[x^2-13x+22=(x-2)(x-11)\]
triciaal
  • triciaal
factor the denominator again hint 2*11 = 22 and 2 + 11 = 13
misty1212
  • misty1212
then cancel and you get what you wrote
anonymous
  • anonymous
But what would be the restrictions?
misty1212
  • misty1212
so your answer is correct as for the "restrictions" the denominator cannot be zero
misty1212
  • misty1212
\[(x-2)(x-11)=0\\ x=2,x=11\]
misty1212
  • misty1212
so the restrictions are \(x\neq2\) and \(x\neq 11\) because if \(x\) where either of those two numbers, the denominator would be zero, and if you try to divide by zero you will explode
anonymous
  • anonymous
Ok. I need to ask another one
anonymous
  • anonymous
Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the variable.
misty1212
  • misty1212
lol the equation tool below is very useful
anonymous
  • anonymous
I got x-5/x+1
anonymous
  • anonymous
Sorry
misty1212
  • misty1212
\[\huge \frac{x^2+4x-45}{x^2+10x+9}\]
misty1212
  • misty1212
your answer is correct
anonymous
  • anonymous
yes:) What would be the restrictions for this one? My answer is x-5/x+1
misty1212
  • misty1212
repeat as before take the denominator in factored form set it equal to zero, solve for \(x\)
anonymous
  • anonymous
x=-1?
misty1212
  • misty1212
you obviously already factored the denominator as \[(x+1)(x+9)\] solve \[(x+1)(x+9)=0\] and solve for \(x\)
anonymous
  • anonymous
-1,-9
misty1212
  • misty1212
bingo
misty1212
  • misty1212
that is, those are the restricted values
anonymous
  • anonymous
ohh thank you:)
anonymous
  • anonymous
That's all for now
anonymous
  • anonymous
Simplify completely quantity 6 x minus 12 over 10.
anonymous
  • anonymous
is it 3(x-5)/5

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