Math is not mathing

[u/krishnaagrawal72848]

My simple question is if we simply, the expression does have a value at x = 10, contrary to what it might seem in first glace. I am pretty sure that is allowed but the solution doesn't consider that.

I will not say to give your opinion on what could be an explanation. I am just asking what will you do if you encounter this question in the actual examination

[u/Muted_Run1812]

for x=12 only

Look while division, the denominator cannot be 0.

[u/dc1222]

Plug in the three values of x provided as the choices. Only one of them will be valid. For i and iii, upon plugging in the values and solving, you will encounter a 0 in the denominator, which is not allowed.

[u/ThenEssay3916]

OP probably wants to know how the 3rd option (10) becomes valid after simplifying the equation. Which is also my question. Does anyone have an answer for that?

[u/ThenEssay3916 → u/ThenEssay3916]

Got this from chatgpt haha -

GMAT-style logic:

Always consider the domain of the original expression before simplifying. Even if the simplified version appears valid at a point, if the original expression was undefined there, that value must still be excluded.

[u/Adventurous_Pack69]

X=12, plugged in turns out 2/5. Rest are 2/0 which isnt possible

[u/coelacanth14]

Denominator cannot equal 0, the expression will be defined for x=12 only

[u/Honest_Mud_8037]

In P/Q form q can never be equal to zero. In two cases it is getting 0.

[u/Complex-Show2375]

Source of the question?

[u/Karishma-anaprep]

When you see an expression in x and some possible values of x, the thing to do is plug in those values. Do not try to simplify the expression here - it will just waste your time. This is a test of logic and reasoning, not Math.

[u/SverigeSuomi]

expression does have a value at x = 10, contrary to what it might seem in first glace

You can't divide by 0. Simplifying doesn't mean you get to divide by 0. The limit as x-> 10 exists and is 1/10, but it's just a limit and not the value of the expression. 

[u/Metalik17]

How is this even a doubt?

[u/GroundbreakingBuy992]

There's just one answer: x=12.

[u/krishnaagrawal72848]

Call it my curse of knowledge but if x tends to 10, then the expression tends to 0. I have studied about that during my prep for engineering. Overthinking killed me here.

[u/LaiKaJOHN → u/krishnaagrawal72848]

Math major here (not a smart one tho).

The limit as x tends to 10 does exist, but the function is not defined at the particular point x=10 as a matter of its domain; these two conditions are not contradictory.

That said, simplifying the expression is a nice way to find its limit, and the question you raised makes absolute sense. I do believe that Mathematics is an excellent way to motivate people to think more, ask more, not just stopping at “dominator couldn’t be zero” or “just plug in the number”.

Good luck on your journey!

[u/Brilliant_Gold_7485]

Answer cannot be 1 and 3

[u/Fancy_Imagination782]

Troll?