Question

(1/x-3 + 4/x) / (4/x - 1/x-3)

Answer 1

\[\frac{\frac{1}{x}-3+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x}-3} * \frac{x}{x} = \rightarrow simplify \rightarrow = \frac{3x-5}{3x-3}\]

Answer 2

The trick with these uber complex rational expressions is to reduce the whole thing to an expression with only one fraction bar.
Starting on the top:
1/x-3 + 4/x, this is equal to
(x + 4x - 12)/x(x - 3)
(5x - 12)/x(x - 3), we'll put this to one side...

At the bottom:
4/x - 1/x-3, this is equal to
(4x - 12 - x)/x(x - 3)
(3x - 12)/x(x - 3), this is our denominator.

So that entire expression is:
[(5x - 12)/x(x-3)] / [(3x - 12)/x(x-3)]
This is a bit simpler, but can be further simplified. Since the denominator on top is the same as the denominator on the bottom, they can be cancelled, leaving you with:

(5x - 12)/(3x - 12)

Answer 3

\[ \frac{x}{x} = 1 \], so you can do this anytime

Answer 4

@agentx5 whoops, it appears I have had some difficulty interpreting the smorgasbord of slashes as fraction bars.

Answer 5

no problem, I was about to go, "err wait a minute" Made me double-check too ;-)
^_^
This is why I keep sounding like a broken record when people don't use parenthesis

Answer 6

all the slashes are fraction bars

Answer 7

@zakeyadorsey , is this what you intended to write?

\[ \frac{\frac{1}{x}-3+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x}-3} \]

Answer 8

@zakeyadorsey yes, but I don't know what lies under each fraction bar... I'll admit using one lines for uhh complex expressions leads to ambiguities...

Answer 9

for example:
x / 21 + 3x
is
\[\frac{x}{21}+3x\]

whereas:
x / ( 21 + 3x )
is
\[\frac{x}{21+3x}\]

Answer 10

Make sense? :-)

Answer 11

its 1 over x-3 then + 4 over x

Answer 12

Then refer to my first answer :) And feel free to tell me if something isn't clear, or something is wrong, I'm open to your comments

Answer 13

and that part is the numorator because the denominater is another 4 over x -1 over x-3

Answer 14

but I bet @agentx5 can write it in a clearer manner, I have yet to learn how to write these complex stuff :)

Answer 15

Then this:

\[\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}} \rightarrow simplify \rightarrow \frac{5 x-12}{3 x-12}\]

Answer 16

Can I haz medals if I teach you all how to do this syntax to make it look like that? ^_^

Answer 17

Sure, if I know how to give medals (me = noob on this site)

Answer 18

It's two tags

Answer 19

The first it to make it into an active formula thingy, the LaTeX tags (think HTML tags)

Answer 20

\[ to open

Answer 21

\] to close

Answer 22

Second...

Answer 23

ok i did not know that

Answer 24

and yes you can have a medal

Answer 25

The fraction is created by \frac{numerator}{denominator}

It looks like this all together:
\[ \frac{numerator}{denominator} \]

Answer 26

yes i think

Answer 27

I'm listening intently

Answer 28

Try it! (and if you figure it out a medal would be much appreciated)

This also works for polynomial exponents or subtexts:

\[\frac{x^{2x+1}}{e^{x^4}} \]
\[C_6H_{12}O_6\]

Answer 29

Without the tags:
\frac{x^{2x+1}}{e^{x^4}
C_6H_{12}O_6

Answer 30

ok thanks

Answer 31

now teach me how to give a medal :)

Answer 32

You put the \[ type tags around the text you want to turn into a formula, basically

\frac{}{} is by far the most useful, also sqrt{} (squareroot)

Answer 33

Clicky the "best answer" button :-D

Answer 34

Thanks :)

Answer 35

I hope this helps, this LaTeX stuff should really come with a tutorial lol