Is it possible to divide one rational number by another to obtain an irrational number as the quotient?

Is it possible to divide one rational number by another to obtain an irrational number as the quotient?
It is not possible to divide one rational number by another to obtain an irrational number. A rational number is of the form a/b where a and b are both integers, whereas an irrational is a number which is impossible to express in the previously mentioned way.

Let A=(a/b) and B=(c/d) where A and B are both rational numbers. Consider the quotient A/B, this is the same as A(1/B). Rewrite this as (a/b)x(d/c). Assuming we all know basic arithmetic with fractions we can clearly see that the dividend is axd and the divisor is bxc, and the new expression is (axd)/(bxc). Since a, b, c, and d are all integers and the integers are closed under multiplication (two integers multiplied by each other produce another integer) our new expression as a single fraction is one integer over another and it is therefore a rational number.