Solve (x+2)(x+3)-(x+4)^2/2x=

$$( x + 2 ) ( x + 3 ) - \frac { ( x + 4 ) ^ { 2 } } { 2 x } =$$

Evaluate

$$x^{2}+\frac{9x}{2}+2-\frac{8}{x}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$x^{2}+5x+6-\frac{\left(x+4\right)^{2}}{2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+5x+6 times \frac{2x}{2x}.

$$\frac{\left(x^{2}+5x+6\right)\times 2x}{2x}-\frac{\left(x+4\right)^{2}}{2x}$$

Since \frac{\left(x^{2}+5x+6\right)\times 2x}{2x} and \frac{\left(x+4\right)^{2}}{2x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x^{2}+5x+6\right)\times 2x-\left(x+4\right)^{2}}{2x}$$

Do the multiplications in \left(x^{2}+5x+6\right)\times 2x-\left(x+4\right)^{2}.

$$\frac{2x^{3}+10x^{2}+12x-x^{2}-8x-16}{2x}$$

Combine like terms in 2x^{3}+10x^{2}+12x-x^{2}-8x-16.

$$\frac{2x^{3}+9x^{2}+4x-16}{2x}$$

Expand

$$x^{2}+\frac{9x}{2}+2-\frac{8}{x}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$x^{2}+5x+6-\frac{\left(x+4\right)^{2}}{2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+5x+6 times \frac{2x}{2x}.

$$\frac{\left(x^{2}+5x+6\right)\times 2x}{2x}-\frac{\left(x+4\right)^{2}}{2x}$$

Since \frac{\left(x^{2}+5x+6\right)\times 2x}{2x} and \frac{\left(x+4\right)^{2}}{2x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x^{2}+5x+6\right)\times 2x-\left(x+4\right)^{2}}{2x}$$

Do the multiplications in \left(x^{2}+5x+6\right)\times 2x-\left(x+4\right)^{2}.

$$\frac{2x^{3}+10x^{2}+12x-x^{2}-8x-16}{2x}$$

Combine like terms in 2x^{3}+10x^{2}+12x-x^{2}-8x-16.

$$\frac{2x^{3}+9x^{2}+4x-16}{2x}$$