Solving Rational Equations: Extraneous & Negative Exponents

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

The LCD is the smallest expression that can be used to eliminate the denominators in a set of rational expressions.

$$\frac{1}{a}$$ .

x = -3.

The first step is to find the least common denominator (LCD) and multiply both sides of the equation by it to eliminate the fractions.

No Solution.

It means substituting the found solutions back into the original equation to verify if they hold true.

The LCD is $$x(x + 5)$$ .

The result is $$a$$ .