Solve 2/x^2-1-1/x-1

$$\frac{ 2 }{ { x }^{ 2 } -1 } - \frac{ 1 }{ x-1 }$$

Evaluate

$$-\frac{1}{x+1}$$

Short Solution Steps

Factor x^{2}-1.

$$\frac{2}{\left(x-1\right)\left(x+1\right)}-\frac{1}{x-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{x-1} times \frac{x+1}{x+1}.

$$\frac{2}{\left(x-1\right)\left(x+1\right)}-\frac{x+1}{\left(x-1\right)\left(x+1\right)}$$

Since \frac{2}{\left(x-1\right)\left(x+1\right)} and \frac{x+1}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

Do the multiplications in 2-\left(x+1\right).

$$\frac{2-x-1}{\left(x-1\right)\left(x+1\right)}$$

Combine like terms in 2-x-1.

$$\frac{1-x}{\left(x-1\right)\left(x+1\right)}$$

Extract the negative sign in 1-x.

$$\frac{-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{-1}{x+1}$$

Differentiate w.r.t. x

$$\frac{1}{\left(x+1\right)^{2}}$$