# Write each expression as a singie logarithms. \ln{(\frac{x}{x-1})}

Write each expression as a singie logarithms.
$\mathrm{ln}\left\{\left(\frac{x}{x-1}\right)\right\}+\mathrm{ln}\left\{\left(\frac{x+1}{x}\right)\right\}-\mathrm{ln}\left\{\left({x}^{2}-2\right)\right\}$
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STEP 1
Write down the each expression as a singie logarithms.
Using $\mathrm{ln}\left\{m\right\}+\mathrm{ln}\left\{n\right\}=\mathrm{ln}\left\{\left(mn\right)\right\}$
$\mathrm{ln}\left\{m\right\}-\mathrm{ln}\left\{n\right\}=\mathrm{ln}\left\{\left(\frac{m}{n}\right)\right\}$
STEP 2
$\mathrm{ln}\left\{\left(\frac{x}{x-1}\right)\right\}+\mathrm{ln}\left\{\left(\frac{x+1}{x}\right)\right\}-\mathrm{ln}\left\{\left({x}^{2}-1\right)\right\}$
$\mathrm{ln}\left\{\left(\frac{x}{x-1}×\frac{x+1}{x}\right)\right\}-\mathrm{ln}\left\{\left({x}^{2}-1\right)\right\}$
$\mathrm{ln}\left\{\left(\frac{x+1}{x-1}\right)\right\}-\mathrm{ln}\left\{\left({x}^{2}-1\right)\right\}$
$\mathrm{ln}\left\{\left(\frac{x+1}{\left(x-1\right)\left({x}^{2}-1\right)}\right)\right\}$
$\mathrm{ln}\left\{\left(\frac{x+1}{\left(x-1\right)\left(x-1\right)\left(x+1\right)}\right)\right\}$
$\mathrm{ln}\left\{\left(\frac{1}{{\left(x-1\right)}^{2}}\right)\right\}$