# Division of Rational Functions

Just like rational number division (division of regular fractions), multiply the inverse or the reciprocal. This process is also called "INVERT AND MULTIPLY." For example, suppose you had to divide 1/2 by 3/7. The typical procedure reminds us to "never mind the reason why, just invert and multiply." So following that rule you multiply 1/2 times 7/3 to arrive at the answer of 7/6. This same procedure can be used to divide rational functions.

Sample:

$$\frac{(x + 1)}{(x + 3)} \div \frac{(3x + 3)}{(x - 2)}$$

1) Invert right side fraction.

The right side fraction should then look like this: $$\frac{(x - 2)}{(3x + 3)}$$

2) Replace division symbol with multiplication symbol (remember, never mind the reason why, just invert and multiply).

3) Multiply numerator by numerator and denominator by denominator using the FOIL method.

Numerators: $$(x + 1)*(x - 2)$$ becomes $$x^2 - x - 2$$

Denominators: $$(x + 3)*(3x + 3)$$ becomes $$3x^2 + 12x + 9$$

4) Reduce fraction (if needed)

$$\frac{(x^2 - x - 2)}{(3x^2 + 12x + 9)}$$