anonymous
  • anonymous
"If x>2, then x^2-x-6/x^2-4=??" (Please show your work, Thanks!)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
what do you get when you factor the numerator?
anonymous
  • anonymous
Umm...hehe...Don't the two x^2's cancel each other out...? (sorry... :/ )
jim_thompson5910
  • jim_thompson5910
no that's a common misconception, but they don't

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anonymous
  • anonymous
no
jim_thompson5910
  • jim_thompson5910
what two numbers multiply to -6 and add to -1?
jim_thompson5910
  • jim_thompson5910
if you're not sure, list out the possible ways to factor -6 -6 = -6*1 -6 = -3*2 -6 = -2*3 -6 = -1*6 now which pair of factors add to -1 ?
anonymous
  • anonymous
-2*3
jim_thompson5910
  • jim_thompson5910
close
jim_thompson5910
  • jim_thompson5910
-2+3 = 1 not -1
anonymous
  • anonymous
OH the other one: -3*2 but why -6 and -1?
jim_thompson5910
  • jim_thompson5910
I was just listing all the possible ways to multiply two whole numbers to get -6
jim_thompson5910
  • jim_thompson5910
yes -3+2 = -1
jim_thompson5910
  • jim_thompson5910
the two numbers are -3 and 2 so x^2 - x - 6 factors to (x-3)(x+2)
jim_thompson5910
  • jim_thompson5910
now do the same for x^2-4 and think of x^2-4 as x^2+0x-4
anonymous
  • anonymous
For Numerator u can always use this formula for solving such equations: ax^2+bx+c=0 then roots are x=[-b+Squrt(b^2-4ac)]/2a & [-b-sqrt(b^2-4ac)]/2a For Denominator There is an identity x^2-a^2=(x+a)(x-a) Then cancel out the common terms This should help
jim_thompson5910
  • jim_thompson5910
so what do you get when you factor x^2-4 or x^2+0x-4
anonymous
  • anonymous
So...now find a factor for -4?
jim_thompson5910
  • jim_thompson5910
correct list all the possible ways to multiply to -4
jim_thompson5910
  • jim_thompson5910
see which factorization pair adds to 0
anonymous
  • anonymous
Proceed @jim_thompson5910 is saying right now but after completing this sum . Remember those identities . it will be helpful for future problem solving
anonymous
  • anonymous
2*-2= -4 and 2+(-2)=0
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
so x^2 - 4 factors to (x+2)(x-2)
jim_thompson5910
  • jim_thompson5910
you now have (x-3)(x+2) ---------- (x+2)(x-2)
jim_thompson5910
  • jim_thompson5910
I'm sure you see what cancels
anonymous
  • anonymous
(x+2)/(x-2) cancels
anonymous
  • anonymous
so now left with (x-3)/(x+2)?
jim_thompson5910
  • jim_thompson5910
the x+2 terms cancel I think you meant to say
jim_thompson5910
  • jim_thompson5910
only identical terms can cancel because x/x = 1
anonymous
  • anonymous
right, sorry
jim_thompson5910
  • jim_thompson5910
so you're left with x-3 ------- x-2
anonymous
  • anonymous
Kay
anonymous
  • anonymous
Thanks a lot @jim_thompson5910 ! Really appreciate it!
anonymous
  • anonymous
Now u can have a look at these :)
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jim_thompson5910
  • jim_thompson5910
you're welcome

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