Question

Well, we found another one:) 4/x+2 - 1/x = 2x-1/x2 (that is squared) + 2x.

Answer 1

\[{4 \over x+2} - {1 \over x} = {2x -1 \over x^2 + 2x}\]

So start by putting each of the fractions over a common denominator.

Answer 2

Ok, I will start doing that and get back with you:) Thank you!

Answer 3

Umm, should x or x\[^{x2}\] +2x be the common denominator?

Answer 4

It keeps messing my numbers up. x or x2 plus 2x

Answer 5

I think \[x^2 + 2x\] will be the common denominator.

Answer 6

We are trying to work it, so you do not think I left:)

Answer 7

No problem =)

Answer 8

Is is possible to get the next step?

Answer 9

The next step would be to combine the two fractions on the left side.

Answer 10

Did you get the new form yet?

Answer 11

Ok, we got that part down:)

Answer 12

So what do you have now?

Answer 13

4x2 + 8x - x2 - 2x = 2x-1

Answer 14

That doesn't look quite right.

Answer 15

\[{4 \over x+2} = {4x \over x(x+2)} = {4x \over x^2+2x}\]

\[{-1 \over x} = {-1(x+2) \over x(x+2)} = {-x -2 \over x^2+2x}\]
\[\implies {4 \over x+2} - {1 \over x} = {4x -x -2\over x^2+2x}\]

Answer 16

WOW! How did you even get that to work? I will write it down and be right back.

Answer 17

You do what you do for regular fractions. Figure out what factors you need to multiply by top and bottom to get the denominator you want.

Since x+2 needs a factor of x to become \(x^2 + 2x\) we multiply top and bottom of that fraction by x.

Since x needs a factor of x+2 to become\(x^2 + 2x\) we multiply top and bottom of that fraction by (x+2)

Answer 18

I know this sounds bad, but what is the next step?

Answer 19

Well you have something that looks like this now right?

\[{4x -x -2\over x^2+2x} ={2x -1 \over x^2 + 2x} \]

Start by combining the sum you have on the left side there.

Answer 20

Ok:)

Answer 21

So what do you have?

Answer 22

x=1

Answer 23

Sounds about right.

Answer 24

Wait no.

Answer 25

Almost tricked me.

Answer 26

Oh wait. that is right. I tricked myself!

Answer 27

Just goes to show. Don't do things only in your head ;)

Answer 28

yea!!! God is so good, thatnk you!! I do not know how you are able to keep up with this stuff save for divine grace. You are a math expert!

Answer 29

Again, happy to help. =)

Answer 30

Can we give u another one?

Answer 31

x/2 + 2x-1/3 = 9

Answer 32

Same type deal. need a common denominator.

Answer 33

is it 6?

Answer 34

Oh, and is it
\[{x \over 2} + {2x-1 \over 3} = 9\]?

Answer 35

Yes it is!

Answer 36

Parentheses help disambiguate.

Answer 37

Ok then yes, common denominator is 6.

Answer 38

So what would you multiply the top and bottom of the first fraction by to get a 6 in the denominator?

Answer 39

3 and 2

Answer 40

Yeah, 2 for the second one. You may as well also put the 9 over a 6 denominator while you're at it. Makes things easier.

Answer 41

should it be 9*6?

Answer 42

Yep

Answer 43

So what have you got now?

Answer 44

ok, so if the problem turns out to be 6x+12-6=54 what will the bottom numbers be?

Answer 45

Should be 6x + 12x - 6 = 54, and on bottom you will have all 6's (by design)

Answer 46

So you can actually just ignore the denominators now.

Answer 47

\[{6x + 12x - 6 \over 6} = {54 \over 6} \implies 6x + 12x - 6 = 54\]

Answer 48

Ok, we have that part.

Answer 49

So now it's just a matter of isolating your x and dividing away the coefficient.

Answer 50

We tried that, but we got 18x=60. Is that right?

Answer 51

Yes.

Answer 52

Wait, something is wrong.

Answer 53

Would you mind providing the next step? We cannot get it right.

Answer 54

Well the next step should be to divide both sides by 18, but I think we have a mistake further back.

Answer 55

\[{x \over 2} + {2x-1 \over 3} = 9\]\[\implies {x \over 2}(\frac{3}{3}) + {(2x-1) \over 3}(\frac{2}{2}) = 9(\frac{6}{6})\]\[\implies {3x + 2(2x - 1) \over 6} = {54 \over 6} \]\[ \implies {3x + 4x - 2 \over 6} = {54 \over 6} \]\[\implies 3x + 4x - 2 = 54\]

Answer 56

That's better. Somehow I didn't notice that you'd goofed your denominator conversion.

Answer 57

7x=56? x=8?

Answer 58

Indeed.

Answer 59

You have the basic stuff down. You need to practice your conversion of fractions.

Answer 60

Praise God that we got the right answer!
Thank you again! I think that is all. God bless

Answer 61

Knowing what you did wrong is more important than getting it right. Be sure to look over your solution and see what went wrong.

Answer 62

And why it's not correct.

Answer 63

We will do that. Thank you again! God bless