Math Fractional equations Domain of a function

# Domain of a function

For a fractional equation, the domain of a function specifies which values cannot be used for the variable.

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### Hint

Division by zero is not allowed in mathematics.

To avoid dividing by zero in a fractional equation, you specify the domain of a function. If the result is included in the domain, the solution is valid.

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### Method

1. Write denominator of each fraction and set it equal to zero
2. Dissolve after the variable
3. Specify domain of a function, exclude calculated numbers

### Example

Give the domain of the fractional equation: $\frac{2x}{x-6}=4$

1. #### Write denominator of each fraction and set it equal to zero

$x-6=0$
2. #### Dissolve after the variable

$x-6=0\quad|+6$
$x=6$
=> $x$ can not be 6, otherwise it divides by 0
3. #### Specify domain

The domain of a function is all the real numbers except the 6.
$\mathbb{D}=\mathbb{R}\backslash\{6\}$