Operations with Rational Expressions Flashcard

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

To add rational expressions with different denominators, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

The first step is to find a common denominator for the expressions being subtracted.

To multiply two rational expressions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for two or more rational expressions.

The LCD of $$\frac{1}{x}$$ and $$\frac{1}{x^2}$$ is $$x^2$$ .

The result is $$\frac{2x^2 + 7x - 15}{(x-5)(x+2)}$$ .

The result is $$\frac{x-9}{6x(5x-2)}$$ .

The result is $$\frac{6x - 5xy}{5y}$$ .