Solve left(x-3x/x+1right)/frac{x-2{left(x^+1right)^2}}

$$\frac{ \left( x- \frac{ 3x }{ x+1 } \right) }{ \frac{ x-2 }{ { \left( { x }^{ } +1 \right) }^{ 2 } } }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{x\left(x+1\right)}{x+1}-\frac{3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Since \frac{x\left(x+1\right)}{x+1} and \frac{3x}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x+1\right)-3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Do the multiplications in x\left(x+1\right)-3x.

$$\frac{\frac{x^{2}+x-3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Combine like terms in x^{2}+x-3x.

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

Calculate x to the power of 1 and get x.

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

Divide \frac{x^{2}-2x}{x+1} by \frac{x-2}{\left(x+1\right)^{2}} by multiplying \frac{x^{2}-2x}{x+1} by the reciprocal of \frac{x-2}{\left(x+1\right)^{2}}.

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

Cancel out x+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

$$x^{2}+x$$

Expand

$$x^{2}+x$$

Short Solution Steps

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

$$\frac{\frac{x\left(x+1\right)}{x+1}-\frac{3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Since \frac{x\left(x+1\right)}{x+1} and \frac{3x}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x+1\right)-3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Do the multiplications in x\left(x+1\right)-3x.

$$\frac{\frac{x^{2}+x-3x}{x+1}}{\frac{x-2}{\left(x^{1}+1\right)^{2}}}$$

Combine like terms in x^{2}+x-3x.

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

Calculate x to the power of 1 and get x.

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

Divide \frac{x^{2}-2x}{x+1} by \frac{x-2}{\left(x+1\right)^{2}} by multiplying \frac{x^{2}-2x}{x+1} by the reciprocal of \frac{x-2}{\left(x+1\right)^{2}}.

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

Cancel out x+1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

$$x^{2}+x$$