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

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

Evaluate

$$-x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{1-x}{1-x}.

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

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

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

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

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

Combine like terms in x-x^{2}-1-x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1+x^{2}}{1+x^{2}}.

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

Since \frac{2}{1+x^{2}} and \frac{1+x^{2}}{1+x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in 2-1-x^{2}.

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

Multiply \frac{-x^{2}-1}{1-x} times \frac{1-x^{2}}{1+x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in -x^{2}-1.

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

Cancel out x^{2}+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

Cancel out -x+1 in both numerator and denominator.

$$-\left(-1\right)\left(-x-1\right)$$

Expand the expression.

$$-x-1$$

Expand

$$-x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{1-x}{1-x}.

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

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

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

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

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

Combine like terms in x-x^{2}-1-x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1+x^{2}}{1+x^{2}}.

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

Since \frac{2}{1+x^{2}} and \frac{1+x^{2}}{1+x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in 2-1-x^{2}.

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

Multiply \frac{-x^{2}-1}{1-x} times \frac{1-x^{2}}{1+x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in -x^{2}-1.

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

Cancel out x^{2}+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

Cancel out -x+1 in both numerator and denominator.

$$-\left(-1\right)\left(-x-1\right)$$

Expand the expression.

$$-x-1$$