Arithmetically showing that $\frac{\mathrm{log}(x+1)}{\mathrm{log}\left(x\right)}<\frac{x+1}{x}$

Is there a possibility that this can be shown arithmetically? By arithmetically, I mean not looking at the graph.

$\frac{\mathrm{log}(x+1)}{\mathrm{log}\left(x\right)}<\frac{x+1}{x}$

Thank You

Is there a possibility that this can be shown arithmetically? By arithmetically, I mean not looking at the graph.

Thank You