AAC #7 Rational Expressions and Equations

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

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same.

To subtract rational expressions, find a common denominator, subtract the numerators, and simplify.

The first step is to identify any restrictions on the variable that would make the denominator zero.

Multiply both sides by x to get 1 = 2x, then solve for x: $$x = \frac{1}{2}$$ .

The least common denominator is $$x(x+1)$$ .

To divide rational expressions, multiply by the reciprocal of the divisor.

The result is $$\frac{7x-8}{x+5}$$ .

A rational expression is undefined when its denominator equals zero.

You simplify it to $$\frac{x}{2}$$ by dividing the numerator and denominator by 2x.