Solve left(2x^2+xright)*left(x+x^2right)/x+7x+x^2div(2x)

$$\frac{ \left( 2 { x }^{ 2 } +x \right) \times \left( x+ { x }^{ 2 } \right) }{ x } +7x+ { x }^{ 2 } \div (2x)$$

Evaluate

$$2x^{3}+3x^{2}+\frac{17x}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(2x^{2}+x\right)\left(x+x^{2}\right)}{x}.

$$\frac{\left(x+1\right)\left(2x+1\right)x^{2}}{x}+7x+\frac{x^{2}}{2x}$$

Cancel out x in both numerator and denominator.

$$x\left(x+1\right)\left(2x+1\right)+7x+\frac{x^{2}}{2x}$$

Expand the expression.

$$2x^{3}+3x^{2}+x+7x+\frac{x^{2}}{2x}$$

Combine x and 7x to get 8x.

$$2x^{3}+3x^{2}+8x+\frac{x^{2}}{2x}$$

Cancel out x in both numerator and denominator.

$$2x^{3}+3x^{2}+8x+\frac{x}{2}$$

Combine 8x and \frac{x}{2} to get \frac{17}{2}x.

$$2x^{3}+3x^{2}+\frac{17}{2}x$$

Expand

$$2x^{3}+3x^{2}+\frac{17x}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(2x^{2}+x\right)\left(x+x^{2}\right)}{x}.

$$\frac{\left(x+1\right)\left(2x+1\right)x^{2}}{x}+7x+\frac{x^{2}}{2x}$$

Cancel out x in both numerator and denominator.

$$x\left(x+1\right)\left(2x+1\right)+7x+\frac{x^{2}}{2x}$$

Expand the expression.

$$2x^{3}+3x^{2}+x+7x+\frac{x^{2}}{2x}$$

Combine x and 7x to get 8x.

$$2x^{3}+3x^{2}+8x+\frac{x^{2}}{2x}$$

Cancel out x in both numerator and denominator.

$$2x^{3}+3x^{2}+8x+\frac{x}{2}$$

Combine 8x and \frac{x}{2} to get \frac{17}{2}x.

$$2x^{3}+3x^{2}+\frac{17}{2}x$$