Subtracting fractions with exponents that have a negative base

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Feisty

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Hi, I have a workbook that gives a different answer than what I get and I can't figure out why.

The question is:
6 - 3
x x2 (the 2nd x is squared, not x • 2; sorry, can't get superscript option to work); where x = -3; and there are no parenthesis around the x squared or in the question.

So, I think it's 6/-3 - 3/-9 = -18/9 - -3/9 = -15/9 (or -1 and 2/3). The workbook's answer is - 2 and 1/3.

I can see how they could get this answer but I would have to assume the -3/9 is positive ...?
 
Standard Rule: A fraction has THREE signs. Change any TWO, and you have an equivalent fraction.

[math]\dfrac{2}{-3} = -\dfrac{2}{3} = \dfrac{-2}{3} = -\dfrac{-2}{-3}[/math]
Rework your thoughts by first making your live easier. "6/-3" is AMAZINGLY awkward notation. "-6/3" is so much nicer.
 
Thanks for your reply ... I get what you're saying and was just writing the question verbatim for sake of trying to write it clearly.
So I have 6/x - 3/x (2nd x is squared here); x is -3 and there are no parenthesis in the question.

-6/3 - -3/9 = -18/9 - - 3/9 = -15/9 Is this correct? The workbook key says -21/9.
 
Feisty said:
Hi, I have a workbook that gives a different answer than what I get and I can't figure out why.

The question is:
6 - 3
x x2 (the 2nd x is squared, not x • 2; sorry, can't get superscript option to work); where x = -3; and there are no parenthesis around the x squared or in the question.

So, I think it's 6/-3 - 3/-9 = -18/9 - -3/9 = -15/9 (or -1 and 2/3). The workbook's answer is - 2 and 1/3.

I can see how they could get this answer but I would have to assume the -3/9 is positive ...?
Click to expand...
I think you're saying that the expression is [MATH]\frac{6}{x} - \frac{3}{x^2}[/MATH], where [MATH]x = -3[/MATH]. So you want to evaluate [MATH]\frac{6}{-3} - \frac{3}{(-3)^2}[/MATH].

You made only one mistake: [MATH](-3)^2 = 9[/MATH], not [MATH]-9[/MATH]. Do you see that? Fix that, and you'll get the right answer.

As for the rest of your work, you can make it simpler by simplifying each fraction before combining. For example, [MATH]\frac{6}{-3} = -2[/MATH].

By the way, to type your expression without needing anything fancy, you could write "6/x - 3/x^2".
 
Thank-you, and I see what you mean, but I learned that (−3)squared is (-3)(-3)= 9 and -3 squared (no parenthesis) is -3 x 3 = -9
The workbook reviews this concept as well, but then some of its answers don't seem to agree with this teaching.
Your way agrees with the answer key, but is different from my understanding of squaring numbers with and without parenthesis.
Can you help clarify this for me please?

BTW: how can I get the superscript to work so I can write x squared please?
 
In some coding languages, it may well be that -3 * 3 = -9. It is the programmer's responsibility to understand the precedence rules. The "Unary Minus" can be particularly problematic or subtle.
 
Feisty said:
Thank-you, and I see what you mean, but I learned that (−3)squared is (-3)(-3)= 9 and -3 squared (no parenthesis) is -3 x 3 = -9
The workbook reviews this concept as well, but then some of its answers don't seem to agree with this teaching.
Your way agrees with the answer key, but is different from my understanding of squaring numbers with and without parenthesis.
Can you help clarify this for me please?

BTW: how can I get the superscript to work so I can write x squared please?
Click to expand...
I don't understand. I said just what you said you learned, that [MATH](-3)^2 = 9[/MATH]. What you did here was contrary to that.

Are you saying that you took x2 to be -32, without parentheses? That's wrong. [To get those superscripts, I selected the "2" I'd typed, then selected the "x2" button.]

When you replace x with -3, you have to square the entire "-3", not just the "3", so you have to replace "x" with "(-3)", in parentheses, to make sure it is treated as a whole. When x is -3, x2 has to be 9, right? So it's (-3)2.
 
In x^2 you have to square x. There is no debate there, right? If x happens to be -3 you need to square -3. That means compute (-3)^2=9.

Now if you have -x^2, then you have to square x and put a negative sign in front of it.

It is true that x^2 = (x)^2 so there are, if you like, parenthesis around the x.

One last think, it is not a bad idea to ALWAYS replace the value for a variable with parenthesis around the variable. For example if in 2x you want to let x=-3, then you CAN"T write 2-3 = -1. You must write 2(-3)=-6. See how helpful the parenthesis were?
 
Jomo said:
In x^2 you have to square x. There is no debate there, right? If x happens to be -3 you need to square -3. That means compute (-3)^2=9.

Now if you have -x^2, then you have to square x and put a negative sign in front of it.

It is true that x^2 = (x)^2 so there are, if you like, parenthesis around the x.

One last think, it is not a bad idea to ALWAYS replace the value for a variable with parenthesis around the variable. For example if in 2x you want to let x=-3, then you CAN"T write 2-3 = -1. You must write 2(-3)=-6. See how helpful the parenthesis were?
Click to expand...
You said:

"One last think, it is not a bad idea to ALWAYS........"

That's a good thing you "thunked"....................
 
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