Simple Definition of a "Math Restriction" (Layman's Terms)?

[Emperor]

Homework Statement

For which value(s) of x is each expression not defined?

Homework Equations

x^2+3x-6 divided by x^2-x-12

The Attempt at a Solution

The answer that was given turned out to be:

x^2+3x-6 divided by (-4)(x+3)

Restrictions: x ≠ 4,-3

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I'm trying to learn what a restriction is and what the point of them are, but I've only come across complicated answers from all over the web. Some of the questions I've encountered apparently don't have any restrictions at all as well.

If I can learn what these are then Rational Expressions will become that much easier for me, thank you.

 

[LCKurtz]

Homework Statement

For which value(s) of x is each expression not defined?

Homework Equations

x^2+3x-6 divided by x^2-x-12

The Attempt at a Solution

The answer that was given turned out to be:

x^2+3x-6 divided by (-4)(x+3)

Restrictions: x ≠ 4,-3

______________________________________________________________________________

I'm trying to learn what a restriction is and what the point of them are, but I've only come across complicated answers from all over the web. Some of the questions I've encountered apparently don't have any restrictions at all as well.

If I can learn what these are then Rational Expressions will become that much easier for me, thank you.

The common things that restrict the domain for real functions are:
1. Denominator can't be zero (as in this example)
2. Argument under a square root sign can't be negative
3. Argument of logarithm must be non-negative.

 

[HallsofIvy]

Homework Statement

For which value(s) of x is each expression not defined?

Homework Equations

x^2+3x-6 divided by x^2-x-12

The Attempt at a Solution

The answer that was given turned out to be:

x^2+3x-6 divided by (-4)(x+3)

No, it's not. The denominator is (x- 4)(x+ 3).

Restrictions: x ≠ 4,-3

Right- if x= 4 then x- 4= 0. If x= -3 then x+ 3= 0. In either case, (x- 4)(x+ 3) would be 0 and you cannot divide by 0.

______________________________________________________________________________

I'm trying to learn what a restriction is and what the point of them are, but I've only come across complicated answers from all over the web. Some of the questions I've encountered apparently don't have any restrictions at all as well.

If I can learn what these are then Rational Expressions will become that much easier for me, thank you.

For rational expressions, they are all based on the fact that division by 0 is not defined, a simple fact of arithmetic.

For other kinds of functions there may be other restrictions. For example, as long as you are working with the real number system, you cannot take the square root of a negative number. And a logarithm can only be applied to positive numbers.