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\}$