Condense the logarithmic expression $\ln\left(\frac{y+1}{y-1}\right)+\ln\left(\frac{y}{y+1}\right)-\ln\left(y^2+1\right)$

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Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression ln((y+1)/(y-1))+ln(y/(y+1))-ln(y^2+1). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Multiplying fractions \frac{y+1}{y-1} \times \frac{y}{y+1}. Simplify the fraction \frac{\left(y+1\right)y}{\left(y-1\right)\left(y+1\right)} by y+1. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right).