lim x gets close to 25 on 5-squerroot x/ x -25

Question

tkhunny · Answer

Please fix with parenthses.  It is not clear at all what you intended to write.  Is it this: $\dfrac{5-\sqrt{x}}{x-25}$.  If so, please write it again, remember your order of operations.

anonymous · Answer

yes that is what I wanted to write I solved part of it

anonymous · Answer

$$5-\sqrt{x}/x-25 (5+\sqrt{x}/5+\sqrt{x}) = 25 -x /(x-25)(5+\sqrt{x} = 1/5+\sqrt{x}$$

anonymous · Answer

i got 1/10 as the answer, but the back of my book say i has to be negative

tkhunny · Answer

Well, you wrote $4 - \dfrac{\sqrt{x}}{x} - 25$ or maybe $4 - \sqrt{\dfrac{x}{x}-25}$

Sorry, it is quite painful.  You have entierly abandoned the Order of Operations.

tkhunny · Answer

$\dfrac{25-x}{x-25} = -1$

anonymous · Answer

no I wrote $$5-\sqrt{x}/ x-25$$ then I multiplied by a fancy 1 and got

anonymous · Answer

$$25-x/(x-25)(5+\sqrt{x)}$$

tkhunny · Answer

You wrote what you wrote, not what you think you wrote.  There are rules about this sort of thing.  We call these rules the Order of Operations.

$5 - \sqrt{x}/x - 25 = 5 - \dfrac{\sqrt{x}}{x} - 25$

NOT $\dfrac{5-\sqrt{x}}{x-25}$, which is what you intend.

anonymous · Answer

never mind, I know what I did wrong.

tkhunny · Answer

$25 - x/(x-25)(5+\sqrt{x})$ MEANS $25 - \dfrac{x}{x-25}\cdot (5+\sqrt{x})$ and that is NOT what you intend.  You must learn and follow the Order of Operations.  It is not optional.

anonymous · Answer

I just made a typing mistake, I didn't notice that I put a / instead of a (, I intended for a (.

tkhunny · Answer

No, it's WAY worse than that.  It is VERY difficult to communicate if you don't learn the rules that everyone else trying to communicate is trying to use.  From the very beginning of this thread you have ignored the Order of Operations.  You must do better than that.

Anyway, good work on the solution.  Getting it to work in your head is an important part of it.  Communicating it to others is the next step.

anonymous · Answer

I don't know how to enter it correctly in the question box, I tried my best to write it. I know how to write it.

tkhunny · Answer

I believe, based on your correct solution, that you are doing okay.  You're just not quite transitioning to in-line interpretation.  It takes more parentheses to do it in-line.

$\dfrac{x-5}{x+5}$ looks great if we write it on paper with a horizontal vinculum $\dfrac{x-5}{x+5}$,

but as soon as we write it in-line, and use the slanted division symbol, it takes more parentheses to get it right.  (x-5)/(x+5)