What is ln(x/(x-1))+ln((x+1)/x) ?

The solution to ln(x/(x-1))+ln((x+1)/x) is ln((x+1)/(x-1))

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simplify ln(x/(x-1))+ln((x+1)/x)

simplify

ln (\frac{x}{x - 1}) + ln (\frac{x + 1}{x})

ln (\frac{x + 1}{x - 1})

Solution steps

ln (\frac{x}{x - 1}) + ln (\frac{x + 1}{x})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x}{x - 1}) + ln (\frac{x + 1}{x}) = ln (\frac{x}{x - 1} \cdot \frac{x + 1}{x})

= ln (\frac{x}{x - 1} \cdot \frac{x + 1}{x})

Simplify

\frac{x}{x - 1} \cdot \frac{x + 1}{x} : \frac{x + 1}{x - 1}

= ln (\frac{x + 1}{x - 1})

ln (\frac{3}{22})

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

- lo g_{10} (3.98 \cdot 1 0^{- 7})

3.14 + lo g_{10} (\frac{1.875}{0.625})

What is ln(x/(x-1))+ln((x+1)/x) ?
The solution to ln(x/(x-1))+ln((x+1)/x) is ln((x+1)/(x-1))