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

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

Evaluate

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

Short Solution Steps

Factor x-x^{2}. Factor x+x^{2}.

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

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

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

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

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

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

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

Combine like terms in x+1+x-1.

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

Cancel out x in both numerator and denominator.

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

Expand \left(x+1\right)\left(-x+1\right).

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

Differentiate w.r.t. x

$$\frac{4x}{\left(1-x^{2}\right)^{2}}$$