What is ln((x-1)/(x+1))-(2x)/((x^2-1)) ?

The solution to ln((x-1)/(x+1))-(2x)/((x^2-1)) is ln(x-1)-ln(x+1)-(2x)/(x^2-1)

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simplify ln((x-1)/(x+1))-(2x)/((x^2-1))

simplify

ln (\frac{x - 1}{x + 1}) - \frac{2 x}{( x ^{2} - 1 )}

ln (x - 1) - ln (x + 1) - \frac{2 x}{x ^{2} - 1}

Solution steps

ln (\frac{x - 1}{x + 1}) - \frac{2 x}{( x ^{2} - 1 )}

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= ln (x - 1) - ln (x + 1) - \frac{2 x}{x ^{2} - 1}

\frac{1}{20} ln (\frac{33}{28})

lo g_{2} (ab)

\frac{1}{2} lo g_{10} (m) - 3 lo g_{10} (n)

lo g_{9} (\frac{f}{81})

ln (\frac{5}{7 x ^{7} y})

What is ln((x-1)/(x+1))-(2x)/((x^2-1)) ?
The solution to ln((x-1)/(x+1))-(2x)/((x^2-1)) is ln(x-1)-ln(x+1)-(2x)/(x^2-1)