Question

2/x+3 - 2x+3/x-1= 6x-5/x^2+2x-3

Answer 1

Would you like help setting up the solution, or are you just looking for the solution (values of x)?

Answer 2

2/x+3 - 2x+3/x-1= 6x-5/x^2+2x-3

2/x+3 - 2x+3/x-1= 6x-5/(x-1)(x+3)

2/x+3(x-1)(x+3) - 2x+3/x-1(x-1)(x+3)= 6x-5/(x-1)(x+3)(x-1)(x+3)

2(x-1)- (x+3)2x+3= 6x-5

2x-2-2x^2+6x+3=6x-5 (little lost on this part)

I only get number that won't go together
Ex: 2{x^2-7x-5}=0

plus the answer is -6 and -1/2

What mistake did I make?

Answer 3

setting up the solution.

Answer 4

OK, I can help. I just need a quick clarification or two. You used spaces in some places, so it makes me think that, for example, where your equation begins 2/x+3 - ... you might mean 2/(x+3). Which is correct? Is the first fraction "2/x" and then adding 3 to that, or is the first fraction 2 over "x+3"?

Answer 5

OK, since I didn't hear back, I'm going to guess that it's the first case, based on your second post.

Answer 6

2(x-1)

Answer 7

I mean I canceled 2/x+3(x-1)(x+3) into 2(x-1)

Answer 8

Then what you have is 2/(x+3) - (2x+3)/(x-1) = (6x-5)/(x^2+2x-3).

Factoring the denominator on the right-hand side gives

2/(x+3) - (2x+3)/(x-1) = (6x-5)/((x+3)(x-1))

Now, turn the left-hand side into a single fraction by multiplying the first term by (x-1)/(x-1) and the second term by (x+3)/(x+3) ...

Answer 9

That gives ( 2(x-1) - (2x+3)(x+3) ) / ( (x+3) (x-1) ) = (6x-5) / ( (x+3) (x-1) ).

We can now disregard the denominator (except, of course, we must rule out x=-3 and x=1 as possible solutions) to get

2(x-1) - (2x+3)(x+3) = 6x-5.

Answer 10

Combining like terms yields

-2x^2 - 13x - 6 = 0.

Answer 11

I see but how do you get like term since the 2x^2 is a negative plus 13 doesn't have a like term into two.

Answer 12

So I believe the solutions are x = -1/2 and x = -6, but give me a chance to double-check.

Answer 13

alright

Answer 14

sorry for the long help

Answer 15

No problem. Thanks for giving me a chance to check my work. I think it's o.k. Did it help you find the problem? Or do you have any questions?

Answer 16

Oh, and I missed a question while answering. The 2(x-1) - (2x+3)(x+3) = 6x-5 becomes

2x - 2 - (2x^2 + 6x + 3x + 9) = 6x - 5.

Answer 17

little bit, thanks I thought if I can reverse on how to get the answer then the rest is easy. I thought the answer is (x+6)(2x+1)

Answer 18

I trying to figure out why this part on the example
Ex: 2{x^2-7x-5}=0
keep poping up when I put them together

Answer 19

This then becomes

2x - 2 - 2x^2 - 6x - 3x - 9 = 6x - 5.

Subtract 6x from each side:

2x - 2 - 2x^2 - 6x - 3x - 9 - 6x = - 5.

Add 5 to each side:

2x - 2 - 2x^2 - 6x - 3x - 9 - 6x + 5 = 0.

The -2x^2 is all alone, but the other terms can be combined to get

-2x^2 - 13x - 6 = 0.

Answer 20

And yes, the way to get the factored form that you "reversed" to get is this:

-2x^2 - 13x - 6 = 0

Same as:

2x^2 + 13x + 6 = 0

Which factors to:

(2x+1)(x+6) = 0.

So 2x+1=0 would mean x=-1/2, and x+6=0 would mean x=-6.

So you had good ideas, just got lost a little in the details maybe.

Answer 21

on the 2x^2+13+6= 0 part since nothing can't add up to 13
ex: 6X1=6 6+1=7

Answer 22

Well, that's where the 2x (as opposed to just x) comes in. Using FOIL (First, Outside, Inside, Last) on

(2x+1)(x+6)

gets

F: 2x(x) = 2x^2
O: 2x(6) = 12x
I: 1(x) = x
L: 1(6) = 6

The "O" and "I" get you the 13x.

Answer 23

I see now,sorry. I was looking at it at a different view. Thanks :D

Answer 24

You're welcome. Good luck. Bye.