How do you divide rational expressions?

To divide rational expressions, first simplify the expressions and remove extraneous terms, then multiply by the reciprocal. Rational expressions can include terms of different degrees, but to express the solution clearly you need to factor them down.

1. Factor all terms of the expressions

   For example, if you have the expression (x^2 - 5x + 6)/(x^2 + 3x - 2) divided by (x^2 + 3x + 2)/(x + 1), the expressions simplify to (x - 2)(x + 3)/(x - 1)(x - 2) / (x + 1)(x + 2)/(x + 1).

2. Cancel out all like terms

   Any term divided by itself equals one, so those terms can be canceled out. Doing this leaves the expressions written as (x + 3)/(x - 1) / (x + 2)/1.

3. Multiply the first expression by the reciprocal of the second one

   The reciprocal is the result of the numerator and denominator switching places. Doing this yields the result to be (x + 3)/(x - 1)(x + 2). If the situation requires it, you can use the FOIL method to multiply the two terms in the denominator. To do this, multiply the first terms, then the outside ones, then the inside, then the last and combine the results.