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.