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

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

Evaluate

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

Short Solution Steps

Factor 1-x^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1-x and \left(x-1\right)\left(-x-1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{1}{1-x} times \frac{-\left(x+1\right)}{-\left(x+1\right)}. Multiply \frac{2}{\left(x-1\right)\left(-x-1\right)} times \frac{-1}{-1}.

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

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

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

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

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

Combine like terms in -x-1+2.

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

Extract the negative sign in -x+1.

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

Cancel out x-1 in both numerator and denominator.

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

Differentiate w.r.t. x

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