5/x^2+x-2 - 6/x^2+2x-3 Reduce to the lowest terms, simplify.

- anonymous

5/x^2+x-2 - 6/x^2+2x-3 Reduce to the lowest terms, simplify.

- Stacey Warren - Expert brainly.com

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- 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

Do you know how to factor either denominator?

- 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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## More answers

- 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

oh (x-1)(x+1) & then it'd be (x-2)(x+1) ?

- 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

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

Yes.

- anonymous

(x-1 ) (x+ 3)

- Stacey

Very good!

- anonymous

Now I got to multiply the 5 by (x+3) right to make it like dem and then the 6(x+2)

- anonymous

& thank you :D

- Stacey

You are correct.
& your're very welcome.

- anonymous

You're better than my teacher! haha, let me work it out and see what I get

- Stacey

Thanks.

- anonymous

on top :5x+15-6x+12
bottom (x-1)(x+2)(x+3)

- anonymous

-x+27 ?

- Stacey

The bottom is correct.

- Stacey

On top: (5x+15) - (6x+12)
Do you see how that will change your answer a little?

- anonymous

I factor?!

- anonymous

5(x+3) 6(x+2)

- Stacey

Sorry. That was not what I was trying to say.
The minus gets distributed to the 6x and the 12.

- anonymous

oh wait that takes me back to the step before :/

- anonymous

oh yeah

- Stacey

So instead of 5x + 15 - 6x +12, we should have
5x + 15 - 6x - 12.

- anonymous

-x-3 ?

- Stacey

-x + 3

- anonymous

oh cause the 15 is positive

- Stacey

Correct

- anonymous

the x+3 doesn't cancel right, because it has a - infront

- Stacey

Correct. Nothing cancels.

- anonymous

:D

- anonymous

(x^3a+1 y^3b+4) / (y^2b-3 x^2a-1) Sorry! I really want to ace this test :(

- Stacey

Is 3a the first exponent?

- anonymous

yes
x^3a+1 the 3a+1 is the exponent

- Stacey

Oh. That makes more sense.

- 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

Oh yeah then the 3a+1/2a-1 =

- anonymous

3a-2a and then 1-(-1)

- anonymous

Right?

- Stacey

Yes. The x-exponent would be
(3a+1)-(2a-1) = 3a+1-2a+1 = a+2

- anonymous

okay so then 3b+4-2b-3 = b+1

- anonymous

x^a+2 y^b+1 right?

- Stacey

Remember to distribute the minus to the -3.
4-(-3) = 4+3 = 7

- anonymous

o0oo yeah, then x^a+2 y^b+7

- Stacey

Yes.

- Stacey

I am going to go. Good luck on your test.

- anonymous

Thank you appreciate it!

- Stacey

You're very welcome.

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