anonymous
  • anonymous
5/x^2+x-2 - 6/x^2+2x-3 Reduce to the lowest terms, simplify.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Please use parentheses, it really helps clarify which parts of the expression go together in fractions. I'm assuming the expression is (5 / (x^2 + x - 2)) - (6 / (x^2 + 2x - 3)).
Stacey
  • Stacey
Do you know how to factor either denominator?
anonymous
  • anonymous
Sorry, & yeah that's how the expression is. & hm let me try I tried (x+1)(x+1)(x-1) for x^2+x-2 It doesn't look right to me.

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Stacey
  • Stacey
It's not. Since we have x^2, we will only have two parenthesis. Also the third term being negative tells us that we have a plus and a minus. So we know that it factors into (x-__)(x+__)
anonymous
  • anonymous
oh (x-1)(x+1) & then it'd be (x-2)(x+1) ?
Stacey
  • Stacey
To get a -2, we need the blanks must multiply to be 2, but add to be the middle number. For example: (x-1)(x+2)=x^2 + x - 2 because -1*2=-2 and -1 + 2 = 1
anonymous
  • anonymous
oh yeah that makes sense. so for the other equation it has to add up to multiply to -3 but add up to 2 right
anonymous
  • anonymous
Yes.
anonymous
  • anonymous
(x-1 ) (x+ 3)
Stacey
  • Stacey
Very good!
anonymous
  • anonymous
Now I got to multiply the 5 by (x+3) right to make it like dem and then the 6(x+2)
anonymous
  • anonymous
& thank you :D
Stacey
  • Stacey
You are correct. & your're very welcome.
anonymous
  • anonymous
You're better than my teacher! haha, let me work it out and see what I get
Stacey
  • Stacey
Thanks.
anonymous
  • anonymous
on top :5x+15-6x+12 bottom (x-1)(x+2)(x+3)
anonymous
  • anonymous
-x+27 ?
Stacey
  • Stacey
The bottom is correct.
Stacey
  • Stacey
On top: (5x+15) - (6x+12) Do you see how that will change your answer a little?
anonymous
  • anonymous
I factor?!
anonymous
  • anonymous
5(x+3) 6(x+2)
Stacey
  • Stacey
Sorry. That was not what I was trying to say. The minus gets distributed to the 6x and the 12.
anonymous
  • anonymous
oh wait that takes me back to the step before :/
anonymous
  • anonymous
oh yeah
Stacey
  • Stacey
So instead of 5x + 15 - 6x +12, we should have 5x + 15 - 6x - 12.
anonymous
  • anonymous
-x-3 ?
Stacey
  • Stacey
-x + 3
anonymous
  • anonymous
oh cause the 15 is positive
Stacey
  • Stacey
Correct
anonymous
  • anonymous
the x+3 doesn't cancel right, because it has a - infront
Stacey
  • Stacey
Correct. Nothing cancels.
anonymous
  • anonymous
:D
anonymous
  • anonymous
(x^3a+1 y^3b+4) / (y^2b-3 x^2a-1) Sorry! I really want to ace this test :(
Stacey
  • Stacey
Is 3a the first exponent?
anonymous
  • anonymous
yes x^3a+1 the 3a+1 is the exponent
Stacey
  • Stacey
Oh. That makes more sense.
Stacey
  • Stacey
When we divide with variables that are the same, we can subtract exponents. For example, x^12/x^3 = x^(12-3) = x^9
anonymous
  • anonymous
Oh yeah then the 3a+1/2a-1 =
anonymous
  • anonymous
3a-2a and then 1-(-1)
anonymous
  • anonymous
Right?
Stacey
  • Stacey
Yes. The x-exponent would be (3a+1)-(2a-1) = 3a+1-2a+1 = a+2
anonymous
  • anonymous
okay so then 3b+4-2b-3 = b+1
anonymous
  • anonymous
x^a+2 y^b+1 right?
Stacey
  • Stacey
Remember to distribute the minus to the -3. 4-(-3) = 4+3 = 7
anonymous
  • anonymous
o0oo yeah, then x^a+2 y^b+7
Stacey
  • Stacey
Yes.
Stacey
  • Stacey
I am going to go. Good luck on your test.
anonymous
  • anonymous
Thank you appreciate it!
Stacey
  • Stacey
You're very welcome.

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