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Equations with fractions

In an equation with fractions you multiply every term by the common denominator, so that the fractions disappear. Then you solve the new equation as usual. Finally you insert the solution into the original denominators. A value that makes a denominator zero is not a solution, even if it appeared after you multiplied. Write the domain before you start.

\frac{x}{a} + \frac{x}{b} = c

equation with fractions

bx + ax = abc

after multiplying by ab

Symbols

$a,\ b$	the denominators
$c$	the right side

Example

$\dfrac{x}{2} + \dfrac{x}{3} = 5$ . Multiply by 6: $3x + 2x = 30$ , so $x = 6$ .

Check: $\dfrac{6}{2} + \dfrac{6}{3} = 5$ .

Multiply by the common denominator, and discard solutions that make a denominator zero.

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Part of Mathematics S1: Algebra and equations.