Solve (x^2+4/3x+6)(x-2/x+2)

$$( \frac { x ^ { 2 } + 4 } { 3 x + 6 } ) ( \frac { x - 2 } { x + 2 } )$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}+4}{3x+6} times \frac{x-2}{x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+4\right)\left(x-2\right)}{\left(3x+6\right)\left(x+2\right)}$$

Use the distributive property to multiply x^{2}+4 by x-2.

$$\frac{x^{3}-2x^{2}+4x-8}{\left(3x+6\right)\left(x+2\right)}$$

Use the distributive property to multiply 3x+6 by x+2 and combine like terms.

$$\frac{x^{3}-2x^{2}+4x-8}{3x^{2}+12x+12}$$

Expand

$$\frac{x^{3}-2x^{2}+4x-8}{3\left(x+2\right)^{2}}$$

Short Solution Steps

Multiply \frac{x^{2}+4}{3x+6} times \frac{x-2}{x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+4\right)\left(x-2\right)}{\left(3x+6\right)\left(x+2\right)}$$

Use the distributive property to multiply x^{2}+4 by x-2.

$$\frac{x^{3}-2x^{2}+4x-8}{\left(3x+6\right)\left(x+2\right)}$$

Use the distributive property to multiply 3x+6 by x+2 and combine like terms.

$$\frac{x^{3}-2x^{2}+4x-8}{3x^{2}+12x+12}$$