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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Add the numbers:

1 + 1 = 2

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

ln ∣ x ∣ + \frac{1}{x} - \frac{1}{2 x ^{2}} - ln ∣ x + 1 ∣

- lo g_{10} (1.2 \cdot 1 0^{3})

ln (\frac{x ^{2} - 25}{x ^{4}})

\frac{ln ( a )}{2} - ln (b) - 3 ln (c)

ln (\frac{- 4 i}{1 - i})

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