Math Fractions Domain of an algebraic fraction

# The domain of an algebraic fraction

For fraction terms, certain numbers are sometimes not possible to set for a variable, if the denominator assumes the value zero. All permissible insertions are therefore specified as domain $D$.

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### Remember

The domain of a term is the set of numbers for which the term is defined.
It is given as follows:$D=\mathbb{Q}\backslash\{\text{number}\}$ (Domain is all rational numbers without "number")
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### Method

1. Write out the denominator of the fractional term and set it equal to zero
2. Dissolve after the variable
3. Specify the domain, exclude calculated numbers

### Example

Specify the domain of the algebraic fraction: $\frac{15}{x+4}$

1. #### Write out the denominator of the algebraic fraction and set it equal to zero

$x+4=0$
2. #### Dissolve after the variable

$x+4=0\quad|-4$
$x=-4$
=> $x$ cannot be -4, otherwise it is divided by 0
3. #### Specify the domain

The domain is all rational numbers except -4, because if you use -4, the algebraic fraction would be invalid.
$\mathbb{D}=\mathbb{Q}\backslash\{-4\}$