Question

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

Answer 1

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)).

Answer 2

Do you know how to factor either denominator?

Answer 3

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.

Answer 4

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+__)

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

Yes.

Answer 9

(x-1 ) (x+ 3)

Answer 10

Very good!

Answer 11

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

Answer 12

& thank you :D

Answer 13

You are correct.
& your're very welcome.

Answer 14

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

Answer 15

Thanks.

Answer 16

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

Answer 17

-x+27 ?

Answer 18

The bottom is correct.

Answer 19

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

Answer 20

I factor?!

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

oh yeah

Answer 25

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

Answer 26

-x-3 ?

Answer 27

-x + 3

Answer 28

oh cause the 15 is positive

Answer 29

Correct

Answer 30

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

Answer 31

Correct. Nothing cancels.

Answer 32

:D

Answer 33

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

Answer 34

Is 3a the first exponent?

Answer 35

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

Answer 36

Oh. That makes more sense.

Answer 37

When we divide with variables that are the same, we can subtract exponents.
For example, x^12/x^3 = x^(12-3) = x^9

Answer 38

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

Answer 39

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

Answer 40

Right?

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

Yes.

Answer 47

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

Answer 48

Thank you appreciate it!

Answer 49

You're very welcome.