Solve x^3+x^2/6x*3/2x^2+5x=

$$\frac { x ^ { 3 } + x ^ { 2 } } { 6 x } * \frac { 3 } { 2 x ^ { 2 } + 5 x } =$$

Evaluate

$$\frac{x+1}{2\left(2x+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+x^{2}}{6x}.

$$\frac{\left(x+1\right)x^{2}}{6x}\times \frac{3}{2x^{2}+5x}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(x+1\right)}{6}\times \frac{3}{2x^{2}+5x}$$

Multiply \frac{x\left(x+1\right)}{6} times \frac{3}{2x^{2}+5x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+1\right)\times 3}{6\left(2x^{2}+5x\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{x\left(x+1\right)}{2\left(2x^{2}+5x\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x+1\right)}{2x\left(2x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x+1}{2\left(2x+5\right)}$$

Expand the expression.

$$\frac{x+1}{4x+10}$$

Expand

$$\frac{x+1}{2\left(2x+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+x^{2}}{6x}.

$$\frac{\left(x+1\right)x^{2}}{6x}\times \frac{3}{2x^{2}+5x}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(x+1\right)}{6}\times \frac{3}{2x^{2}+5x}$$

Multiply \frac{x\left(x+1\right)}{6} times \frac{3}{2x^{2}+5x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+1\right)\times 3}{6\left(2x^{2}+5x\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{x\left(x+1\right)}{2\left(2x^{2}+5x\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x+1\right)}{2x\left(2x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x+1}{2\left(2x+5\right)}$$

Expand the expression.

$$\frac{x+1}{4x+10}$$