((x+1))/((xe^(x)+e^(x)))
You asked:
Evaluate the expression: \(\frac{x + 1}{x \cdot {e}^{x} + {e}^{x}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{x + 1}{x \cdot {e}^{x} + {e}^{x}} = \frac{x + 1}{x e^{x} + e^{x}} \)
Expanded
\[\frac{x + 1}{x \cdot {e}^{x} + {e}^{x}} = \frac{x}{x e^{x} + e^{x}} + \frac{1}{x e^{x} + e^{x}}\]
Factored
\[\frac{x + 1}{x \cdot {e}^{x} + {e}^{x}} = e^{- x}\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).