AAC #7 Rational Expressions and Equations

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Excluded values are values of the variable that make the denominator zero, which are not allowed in rational expressions.

Set the denominator equal to zero: x - 3 = 0, so the excluded value is x = 3.

Simply add the numerators and keep the same denominator.

Find a common denominator, convert each fraction, and then add the numerators.

Multiply the numerators together and the denominators together.

$$\frac{8}{15}$$ .

Factor the numerator and denominator and cancel out any common factors.

$$\frac{(x-2)(x+2)}{x(x-2)} = \frac{x+2}{x}$$ (for x ≠ 2).

Cross-multiply to eliminate the fractions, then solve the resulting equation.