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← Solving Rational Equations and Inequalities

Concept

Rational Equation

A rational equation is an equation that contains at least one rational expression.

\frac{1}{x} + \frac{x}{2} = \frac{x + 4}{2 x}

If a rational equation is expressed as a proportion, it can be solved by using the Cross Products Property. Otherwise, to eliminate the fractions, each side of the equation is multiplied by the least common denominators of the expressions.

Rational Equation	Method
$\frac{x}{2 x + 7} = \frac{2}{x - 1}$	Cross Products Property
$\frac{x}{x - 5} + \frac{x}{x + 5} = \frac{2}{x ^{2} - 2 5}$	LCD

When a rational equation has been solved using algebraic methods, it is necessary to ensure that each solution satisfies the original equation because extraneous solutions may appear.

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