Math Fractional equations Solving fractional equations

# Solving fractional equations

In solving the fractional equation, the domain of a function is first determined, and then the equation with equivalence transformation is solved.

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### Remember

When fractional equations are solved, the fractional terms are resolved. For that, multiply the whole equation by the denominator.
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### Method

1. Determine domain of a function
2. Solve equation with equivalence transformation
3. Check result

### Example

Solve the following fractional equation: $\frac{4x}{2x+10}=1$

1. #### Determine the domain

$2x+10=0\quad|-10$
$2x=-10\quad|:2$
$x=-5$

$\mathbb{D}=\mathbb{R}\backslash\{-5\}$
2. #### Change equation to $x$

To resolve the fraction terms, the equation is multiplied by the denominator of the fraction.
$\frac{4x}{2x+10}=1\quad|\cdot(2x+10)$
$4x=2x+10\quad|-2x$
$2x=10\quad|:2$
$x=5$
3. #### Check result

Check if the result is included in the domain

$x=5$ is contained in the domain $\mathbb{D}=\mathbb{R}\backslash\{-5\}$: The solution is valid.