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Geek Culture / solve this simple math problem

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Phaelax
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Posted: 10th Apr 2014 02:59 Edited at: 10th Apr 2014 03:00
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My girl took quiz online for school but she showed me this problem because she wasn't sure about it. The answer for Y is suppose to be -14/3 according to the quiz. That's not matching up with what I get, which is the two sides are not actually equal. I even tried putting the equation into a few online solvers and they end up with fraction with a 0 denominator. Thoughts?



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easter bunny
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Posted: 10th Apr 2014 03:27
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In my experience, maths tests often have incorrect answers


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Hockeykid
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Posted: 10th Apr 2014 05:39 Edited at: 10th Apr 2014 05:40
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5/(y-4) - 8/(y-4) = 2/(y^2 - 16)

-3/(y-4) = 2/(y^2 - 16)

Cross multiply

2(y-4) = -3(y^2 - 16)

Divide by (y^2 - 16)

2(y-4)/(y^2 - 16) = -3

(y^2 - 16) is the same as (y-4)(y+4) so

2(y-4)/(y-4)(y+4) = -3

2/(y+4) = -3

Cross multiply again

-3(y+4) = 2

Distribute

-3y - 12 = 2

-3y = 14

y = -14/3

That's how I solved it, however I probably over complicated it a bit.



Sean

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Dark Java Dude 64
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Posted: 10th Apr 2014 06:17
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I just threw -14/3 into the Y variable on my calculator, and subtracted the two sides of the equation from each other. Resulted in zero; so the answer given is correct.

I tried solving it myself, but the quadratic I came up with -3Y^2-2Y+56 looked scary and hard to solve.

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Phaelax
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Posted: 10th Apr 2014 06:46
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Hockeykid, you did pretty much the same steps I did. I don't have my scribbles in front of me, but I think I must've mixed something up on the division. I think if it wasn't for 3 different websites giving me inconclusive answers, I might have double checked my own work again.

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Green Gandalf
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Posted: 10th Apr 2014 14:16
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Quote: "That's not matching up with what I get, which is the two sides are not actually equal."


Then you must have made an arithmetic error - they are the same.

The simple solution is this:

1. Multiply both sides by (y-4) and simplify both sides to get
-3 = 2/(y+4)

2. Then rearrange in the usual way to get
y+4 = -2/3

3. The next step is trivial.



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Hawkblood
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Posted: 12th Apr 2014 04:48
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Invert both sides:
(y-4)/5 - (y-4)/8 = (y^2-16)/2

then break it apart:

y/5 - 4/5 - y/8 - 4/8 = y^2/2 -16/2

rearrange:

y/5 - y/8 - y^2/2 = 4/5 + 1/2 - 8

multiply by the common denominator (40)

8y - 5y - 20y^2 = 32 + 20 - 320

rearrange:

-20y^2 + 3y + 268 = 0

this is a quadratic equation, so solve for it:

y= (-b +/- sqrt(b^2 -4ac))/2a
y= -3.586 or 3.736

The fastest code is the code never written.
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Green Gandalf
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Posted: 12th Apr 2014 17:40
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Quote: "Invert both sides:
(y-4)/5 - (y-4)/8 = (y^2-16)/2"


Ouch! Elementary error at the start. You can invert both sides - but you need to do it right.



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Hawkblood
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Posted: 12th Apr 2014 21:56
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Not the first time I've inverted when I should have cross multiplied...

The fastest code is the code never written.
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Green Gandalf
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Posted: 12th Apr 2014 23:07
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You could do either - but your inversion of the left hand side was implemented incorrectly.

Try this simple example where, hopefully (), we can all agree on the answer:

1/2 + 1/2 = 1

Now invert using your method to get:

2/1 + 2/1 = 1

Now that ain't right is it?

Your mistake was to invert each term on the left hand side individually whereas you should have inverted the whole expression - and it helps to simplify the left hand side first.



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Neuro Fuzzy
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Posted: 25th Apr 2014 06:42
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The online solvers I tried show the correct solution
http://www.wolframalpha.com/input/?i=5%2F%28y-4%29-8%2F%28y-4%29%3D%3D2%2F%28y%5E2-16%29
(the key to this problem is recognizing that y^2-16=(y+4)(y-4) )


"I <3 u 2 bbz" - Dark Frager
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BiggAdd
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Posted: 25th Apr 2014 12:18 Edited at: 25th Apr 2014 12:19
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Quote: "The online solvers I tried show the correct solution"

You Chet!

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Dark Java Dude 64
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Posted: 25th Apr 2014 14:05
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Ooooh the King is littering his kingdom with foul language containing content from the lowly external Internet world.

The King. He chet.

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Libervurto
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Posted: 26th Apr 2014 02:32
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Neuro is right that the key is (a+b)(a-b) = a²-b²

My solution attached -->

Formerly OBese87.

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