Question

solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not.

Answer 1

@zepdrix ^-^

Answer 2

Use LaTeX to post the equation.

Answer 3

ok just gimme a sec

Answer 4

Stop being so sloppy >:(
At least use brackets lol

Answer 5

\[\frac{ 4 }{ x-4 } = \frac{ x }{ x-4 } - \frac{ 4 }{ 3 }\]

Answer 6

lol I don't wanna make you wait though ;-; so i just end up doing the equation maker after

Answer 7

You want to multiply both sides of the equation by the `Least Common Multiple`.
Don't worry about common denominator, just multiply all the denominators out of there.

Answer 8

4/(x - 4) = x/(x -4) - 4/3

4/(x - 4) - x/(x - 4) = - 4/3

( 4 - x)/(x - 4) = - 4/3

- (x - 4)/(x - 4) = - 4/3 no solution

x = 4, extraneous

Answer 9

ok....well I'll do the work but thanks chealyn lol

Answer 10

btw zep, can I ask oneee more question?

Answer 11

I'll use brackets this time babe no worries lol

Answer 12

Ok

Answer 13

What is the simplified form of \[\frac{ 3 }{ 4x+3 } + \frac{ 21 }{ 8x^2 + 26x + 15 }\]

Answer 14

uhh I dunno, it looks right to me

Answer 15

I guess you gotta factor some stuff, ya?

Answer 16

8*15 = 120 ish

Answer 17

what

Answer 18

Oh, we have a "hint",
Notice the other denominator is 4x+3,
so this quadratic in the other denominator PROBABLY factors into (4x+3) times something else.

Answer 19

ok...can i show you the options? I think it's B or C but lemme post it

Answer 20

dunno tbh this one is hard

Answer 21

\[\large\rm 8x^2+26x+15\]You'll have to factor this one by grouping.
8*15 = 120.

We need factors of 120 that `add` to 26.

Answer 22

\(\rm 2*60 = 120\)
\(\rm 2+60 \ne26\)

Hmm those didn't work.

Answer 23

http://sketchtoy.com/66414726

Answer 24

ugh ok lemme think

Answer 25

3 * 40 no

Answer 26

4 + 30

Answer 27

* 4 * 30

Answer 28

so -4, +30

Answer 29

No, it's a positive 120, and positive 26, so they both have to be positive

Answer 30

4 and 30 are getting closer though, right?
34 is close to 26,

so we're "close to" the correct factors.

Answer 31

The numbers need to be just a tad closer together.

Answer 32

um

Answer 33

i mean cant you do 30-4

Answer 34

oh wait

Answer 35

its all positive

Answer 36

nvm lol ok so it's 6 and 20

Answer 37

Good good good.
So that's how we'll break down our 26, into 20 and 6.\[\large\rm 8x^2+\color{orangered}{26x}+15\]\[\large\rm 8x^2+\color{orangered}{20x+6x}+15\]And now factor by grouping,\[\large\rm (8x^2+20x)+(6x+15)\]

Answer 38

Remember this process? Lil bit?

Answer 39

yess

Answer 40

but idk what to do now

Answer 41

What can you factor out of the first "group"?
They each have an x in them,
what else they sharing?

Answer 42

an even number? so it'd be 4x^2 + 5x

Answer 43

I'm not just what you just did -_-

You can take an x out of each,\[\large\rm (8x^2+20x)=x(8x^2+20)\]And certainly a 2 out of each (which maybe was what you were trying to do...),
but I think you can take a larger value than a 2 out.

Answer 44

oh my god I just wanna hit myself in the face rn I'm so dumb. It's 11:20 pm rn tho so can i just spit out a guess and you tell me if i'm right?

Answer 45

woops, I took the x out incorrectly :3 hope you noticed that

Answer 46

i did lol

Answer 47

\[\large\rm (8x^2+20x)=4x(2x+5)\]

Answer 48

is it D?

Answer 49

cos the (2x+5)

Answer 50

\[\large\rm (8x^2+20x)+(6x+15)\]\[\large\rm 4x(2x+5)+(6x+15)\]Pulling a 3 out of the other one,\[\large\rm 4x(2x+5)+3(2x+5)\]Factoring further,\[\large\rm (4x+3)(2x+5)\]

Answer 51

Woman I don't know -_-
Don't be lazy lol

Answer 52

it is D!! hahahhaa

Answer 53

aww Zep I'm sorry ;-;

Answer 54

\[\large\rm \frac{ 3 }{ 4x+3 } + \frac{ 21 }{ 8x^2 + 26x + 15 }\]So our expression becomes,\[\large\rm \frac{ 3 }{ 4x+3 } + \frac{ 21 }{(4x+3)(2x+5)}\]

Answer 55

So for common denominator, you need a (2x+5) in the first fraction.

Answer 56

yeayea i just put it in as the answer. anyway thanks so much man!! you're my favorite on here ^-^ have a nice night bb okie? and enjoy the winter weather omg idk how it is in daytona but it's greaaat where I'm at

Answer 57

night~

Answer 58

...le sigh -_-

Answer 59

you .. too -_-

Answer 60

Oh you in FL too? :d

It sucks here right now. Down in the 50's today D:
One day of cold and I'm already hating it haha.