The ratio of subtraction of negative natural exponential function from positive natural exponential function to $2$ is called the hyperbolic sine function.

$e$ is a positive irrational mathematical constant and assume, $x$ is a variable. So, the positive natural exponential function is denoted by $e^x$ and the negative natural exponential function is represented by $e^{-x}$.

The subtraction of negative natural exponential function from positive natural exponential function is written as $e^x\,–\,e^{-x}$.

The ratio of subtraction of them to number $2$ is written as the below mathematical form.

$\large \dfrac{e^x-e^{-x}}{2}$

The ratio of them is called the hyperbolic sine function. The hyperbolic sine is simply written as $\sinh$ in short form but the function is expressed in terms of $x$. Therefore, the hyperbolic sine function is written as $\sinh{x}$ in mathematics.

$\large \sinh{x} = \dfrac{e^x-e^{-x}}{2}$

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