Explanation Division by zero
Consider the expression $\frac{5}{0}$ which shows dividing a number by zero. This division is considered undefined or not possible. This is because, there exists no number $x,$ real or otherwise, such that
$x \cdot 0 = 5.$
Division indicates how many times the denominator "fits" into the numerator. If you calculate $\frac{5}{0}$ to determine how many times $0$ will fit in $5$, you will never reach $5$ no matter how many zeros you try.
$\text{Dividing by $0$ then becomes impossible.}$
Therefore, certain conditions must be specified when s denominator contains a variable. For example,
$\dfrac{5}{a} \quad \quad \text{for } a \neq 0.$
Another way to illustrate why division by $0$ is undefined is to study the graph of $y=\frac{1}{x}.$ By using a table of values some points on the curve can be found.
$x$ 
$\dfrac{1}{x}$ 
$=$

${\color{#0000FF}{\text{}0.5}}$ 
$\dfrac{1}{{\color{#0000FF}{\text{}0.5}}}$ 
${\color{#FF0000}{\text{}2}}$

${\color{#0000FF}{\text{}0.25}}$ 
$\dfrac{1}{{\color{#0000FF}{\text{}0.25}}}$ 
${\color{#FF0000}{\text{}4}}$

${\color{#0000FF}{\text{}0.1}}$ 
$\dfrac{1}{{\color{#0000FF}{\text{}0.1}}}$ 
${\color{#FF0000}{\text{}10}}$

${\color{#0000FF}{0.1}}$ 
$\dfrac{1}{{\color{#0000FF}{0.1}}}$ 
${\color{#009600}{10}}$

${\color{#0000FF}{0.25}}$ 
$\dfrac{1}{{\color{#0000FF}{0.25}}}$ 
${\color{#009600}{4}}$

${\color{#0000FF}{0.5}}$ 
$\dfrac{1}{{\color{#0000FF}{0.5}}}$ 
${\color{#009600}{2}}$

Graphing the points on a coordinate plane allows the behavior of the function to be shown. The red points show what happens as $x$ approaches $0$ from the left, and the green points show what happens as $x$ approaches $0$ from the right.
The closer $x$ comes to $0,$ on both sides, the more extreme the values of the functions become. The quotient approaches $+ \infty$ when $x$ approaches $0$ from the right, and $\text{} \infty$ when $x$ approaches from the left. Because $f(x)=\frac{1}{x}$ is a , $f$ can only produce one value when $x=0.$ Therefore, division by $0$ is undefined.
Suppose dividing by zero was defined. Then, the "logic" below would be accepted as true. Let
$a$ and
$b$ be any real numbers/
$a=b$
$ab=0$
$\dfrac{ab}{ab}=\dfrac{0}{ab}$
$1=0$
Since both sides of the equation are divided by $ab=0,$ and $ab=0,$ the expression was validly manipulated to create a false statement.