Simplification of $x\exp(x)-\exp(x)+x-1$

Question

I have this expression $x\exp(x)-\exp(x)+x-1$.

In my long equation. My question is: is there any way to express this term with simplified mathematical terms, like $\sinh$ or any other function.

$$x\exp(x)-\exp(x)+x-1$$

Answer 1

$$xe^x - e^x + x - 1$$

$$= e^x(x - 1) + (x - 1)$$

$$= (x - 1)(e^x + 1)$$