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

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

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

simplify

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

- ln ((x - 1)^{2})

Solution steps

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

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}) - ln (x^{2} - 1)

Simplify

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

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

Apply log rule:

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

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

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

Simplify

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

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln ((x - 1)^{2})

- 0.4 x + 9.5 = 1.5 x - 0.4

(e^{2 t})^{2}

(a^{2} + 2 a)^{2} - 64

∣ 3 x + x ∣ = 4

∣ x + 3 ∣ = 5

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