Unit 4 Flashcard: Rational Functions Operations

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

To multiply two rational functions, multiply the numerators together and the denominators together.

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

To subtract two rational functions, find a common denominator, rewrite each fraction, and then subtract the numerators.

Finding a common denominator means identifying a common multiple of the denominators of two or more fractions to combine them.

$$x^2 - 49$$ can be factored as $$(x - 7)(x + 7)$$ , which is a difference of squares.

The simplified form is $$\frac{x - 7}{x + 2}$$ .

$$x^2 + 7x + 10$$ can be factored as $$(x + 5)(x + 2)$$ .

The simplified form is $$\frac{x + 2}{x + 1}$$ .

The simplified form is $$-5$$ .