A Problem and a Question

[pepsi_in_a_can]

hi,i'm new to the site, i just have a question

one of the problems in my calculus book asks "why is this wrong?"

and it shows x squared minus 9 divided by x minus 3 equals x plus three.

i dont get whats wrong with the equation,can anyone help?

btw,i'm not sure how to use the symbols here,can someone plz show me?thanks

 

[sydney_bristow87]

:?

I don't see anything wrong with it.

Of course, I did fail my calculus exam, so I'd get a second opinion if I were you.

To use the math symbols, you use the [ tex ] tags (without spaces). Click the thing that says 'forum help' up on that purple top bar and then click 'getting started w/ LaTeX' ... it's helpful.

\(\displaystyle \frac{x^2 - 9}{x-3}\)
factors into

\(\displaystyle \frac{(x + 3)(x - 3)}{x - 3}\)

so then the x - 3's cancel each other out, and you're left with

x + 3 = x + 3

So now, I'm wondering what's wrong with it, too.

 

[Unco]

(x^2 - 9)/(x - 3) = x + 3

is true provided x is not equal to 3, because we have a zero denominator if that is the case.

 

[pepsi_in_a_can]

lol,its driving me nuts,i mean i know sometimes the text books get misprinted but i just think its unlikely.

thanks for showing me how to use the symbols.

 

[pepsi_in_a_can]

(x^2 - 9)/(x - 3) = x + 3

is true provided x is not equal to 3, because we have a zero denominator if that is the case.

i guess if they took the limit when x approaches 3 it would be questionable,but i'm still not sure.

by the way, i like your sig quote.

 

[Unco]

It is called a removable discontinuity.

 

[pepsi_in_a_can]

It is called a removable discontinuity.

so i could just say that when x=3, there is a removeable discontinunity,but while thats true,that doesnt really say what is wrong with the equation.

but thanks for the help so far.

 

[Unco]

It is wrong because it did not state \(\displaystyle \mbox{ x \neq 3}\).

 

[pepsi_in_a_can]

It is wrong because it did not state \(\displaystyle \mbox{ x \neq 3}\).

Good point.Thanks so much for your help.

 

[pka]

so i could just say that when x=3, there is a removeable discontinunity,but while thats true,that doesnt really say what is wrong with the equation.

Yes it does mean it is not an equation.
For an equation the two sides are equal.
The expression (x<SUP>2</SUP>−9)/(x−3) is not the same as (x+3).
The two have different domains.

 

[pepsi_in_a_can]

so i could just say that when x=3, there is a removeable discontinunity,but while thats true,that doesnt really say what is wrong with the equation.

Yes it does mean it is not an equation.
For an equation the two sides are equal.
The expression (x<SUP>2</SUP>−9)/(x−3) is not the same as (x+3).
The two have different domains.

thanks for all the replies and help.