## anonymous 5 years ago u/(u-(u+1/2))=4

1. anonymous

$u\left/\left(u-\left(\frac{1}{2}+u\right)\right)\right.\text{=}4$$u\left/\left(-\frac{1}{2}\right)\right.\text{=}4$$-2 u\text{ = }4$$u\to -2$

2. gw2011

u/[u-(u+1/2)]=4 u/(u-u-1/2)=4 u/-1/2=4 -2u=4 u=-2

3. anonymous

4. gw2011

Either the answer book is wrong or the problems is written incorrectly. Since 1/2 is -1/2, you will get a negative u.

5. gw2011

If you substitute what the answer book has, then the answer will be -4 and not 4.

6. anonymous

well... i'm having trouble writing an equation like this on the computer. but the (u-(u+1/2) is written as u - u +1 over 2.... make sense?

7. gw2011

With the negative in front of (u+1/2), then u becomes -u and the +1/2 becomes -1/2.

8. anonymous

i wish i could figure out the equation thing the u+1 is over the 2. and you're subtracting the whole thing from u...

9. gw2011

If the equation is meant to be the following: u/(u-u+1/2)=4 then u=2 is correct.

10. anonymous

i guess i need to figure out the equation button and re-post my question

11. anonymous

Plug in 2 for u in the problem expression. At the end of the evaluation process Mathematica tells us that -4=+4, an invalid outcome. So u is not 2.$\frac{u}{u-\left(u+\frac{1}{2}\right)}==4\text{/.}u\to 2$$\frac{2}{2-\left(2+\frac{1}{2}\right)}==4$$\frac{2}{2-\frac{5}{2}}==4$$\frac{2}{\left(-\frac{1}{2}\right)}==4$$-4==4$

12. anonymous

the (u+1/2) is not written correctly. it's (u+1)over 2. make sense?

13. gw2011

According to your latest equation that (u+1)/2, then the equation should be as follows: u/[u-(u+1)/2]=4 u/[(2u-u-1)/2=4 u/[(u-1)/2]=4 (u)[2/(u-1)]=4 2u/(u-1)=4 2u=4(u-1) 2u=4u-4 You can rewrite this equation as: 4u-4=2u 2u=4 u=2

14. anonymous

my apologies for mistyping the equation initially

15. anonymous

"the (u+1/2) is not written correctly. it's (u+1)over 2. make sense?" The common convention in computer land is that multiplication and division take precedence over addition and subtraction. So I interpreted the subexpression of concern the way it was presented in my solution derivation. I don't want to ruffle any feathers here, but nearly half the time the math expressions presented as problems on this web site are, strictly speaking, ambiguous. Hence the back and for over what the intent of your problem expression was. Notice that you added an addition ")" after the u+1 that was not in the original problem statement. I use Mathematica 8 for calculations and normally send all math problem statements to WolframAlfa.com for their interpretation of the problem statements. Mathematica 8 has a direct connection with WoframAlfa through a drop down menue selection, " Free- form input" for this purpose. I guess this is an example of "Cloud computing." This is all I have to say on this matter. Have a good day.