Why does $\frac {1}{a}-\frac{1}{b}=\frac {b-a}{ab}$? I really don't understand the expression.
$$\frac {1}{a}-\frac{1}{b}=\frac {b-a}{ab}$$
I generally have a hard time understanding non-intuitive things in math and this is one of them. Normally when I don't understand something I use an app , photomath, to help explain expressions/equations I don't understand however, I still need help with this expression.
I'm told that to get to $\frac {b-a}{ab}$ you need to expand the fraction to the least common denominator:
$$\frac {1}{a}-\frac{1}{b} \to \frac {\pmb b\times 1}{\pmb b a} - \frac {\pmb a \times 1}{\pmb a b} \to \frac {b}{ab} - \frac {a}{ab} \to \frac {b-a}{ab}$$
What I don't understand is this
$$ \frac {\pmb b \times 1}{\pmb b a} - \frac{\pmb a \times 1}{\pmb a b}$$
I don't understand how exactly the $a$ and $b$ seemingly 'appear' in the expression.

$\frac{1}{a}-\frac{1}{b} = \frac{1}{a} * \frac{1}{1} - \frac{1}{b} * \frac{1}{1}$
= $\frac{1}{a} * \frac{b}{b} - \frac{1}{b} *\frac{a}{a}$ = $\frac{b} {ab} - \frac{a}{ab} = \frac{b-a}{ab}$
using $ab=ba$ and $\frac{x}{x} = 1$ for any $x \neq 0$
