Question

How do you simplify this equation?
(1/3-1/x)/(1/6-1/2x)

Answer 1

Start by getting rid of complex fractions. Multiply the top and bottom by 6x.

Answer 2

(x-3)^2/18x^2

Answer 3

Did you just want the answer? Or did you want to know how to do it..

Answer 4

I need to know how to solve it. I'm having really trouble with these kinds of fractions. Please speak to me like I'm an idiot because I have no clue.

Answer 5

Ok, first you know you can always multiply the top and bottom of a fraction by the same thing and you maintain the ratio right?

Answer 6

Oh wait. My bads. I didnt see the division sign.
That explains everything.
(x-3/3x) * (12x/2(x-3)
Your answer is 4

Answer 7

Umm no I don't know what that means. Like I said. I'm an idiot when it comes to this

Answer 8

Because \[{a \over a } = 1 \implies {b\over c} \times 1 = {b\over c} \times {a \over a} \implies {ba \over ca} = {b \over c} \]

Answer 9

ok

Answer 10

Just like you do when you change denominators:

3/4 = 6/8 = 12/16

Answer 11

You can always multiply the top and bottom by the same thing and you maintain the ratio. (you have the same fraction)

Answer 12

Ok. So I'd multiply x by 3 starting at the top half of my equation.

Answer 13

Ok so you have this:
\[{\frac{1}{3}-\frac{1}{x} \over \frac{1}{6} -\frac{1}{2x}} \]

Now if you look at the denominators you have in the fractions on top and bottom you can see that the LCM of all those little fractions is 6x.

Therefore if we multiply the top and bottom of the whole fraction by 6x we will clear those small fractions:

\[{\frac{1}{3}-\frac{1}{x} \over \frac{1}{6} -\frac{1}{2x}} \times \frac{6x}{6x} = \]

Answer 14

\[{6x(\frac{1}{3}-\frac{1}{x}) \over 6x(\frac{1}{6} -\frac{1}{2x})}\]
\[= {6x(\frac{1}{3})-6x(\frac{1}{x}) \over 6x(\frac{1}{6}) -6x(\frac{1}{2x})}\]
\[= {2x - 6 \over x - 3}\]

Answer 15

OOOOOH I see! Ok. Thank you so much!

Answer 16

And from the numerator we can now factor out a 2 and we have:
\[{2(x-3)\over x-3 }= 2,\ \forall x \ne 3\]

Answer 17

Ok what's the upside down A symbol?

Answer 18

That means 'for all'

Answer 19

It means that your original expression is equal to 2 as long as x does not equal 3. If x = 3 then we just divided by 0.

Answer 20

Also I guess x cannot be equal to 0 either.

Answer 21

oh ok. I have to go but this helps me so much.

Answer 22

So technically it should be
\[\forall x \not \in \{0,3\}\]