$\frac{rational}{rational} = irrational$ ?

A rational number is a number which can be represented as fraction $\frac{a}{b}$ where a and b are both integers.
In the question, x= $\frac{a}{b}$ . As they are both rational numbers,we let a= $\frac{c}{d}$ and b= $\frac{e}{f}$ where c, d, e and f are integers.
Substituting these 2 equations into x= $\frac{a}{b}$ , we get x= $\frac{c/d}{e/f}$
Multiplying the denominator and numerator by df, we get x= $\frac{cf}{de}$ . As c, d, e, and f are all intgers, x= $\frac{cf}{de}$ is always a rationl number.

By the definition of rational numbers, all rational numbers can be written as a fraction $\dfrac{a}{b}$ of two integers $a,b$ where $b \ne 0$ . Hence $x$ is always a rational number.