Solve (x+3)^3/(x+2)^3*x^2+4x+4/x^2+6x+0

$$\frac { ( x + 3 ) ^ { 3 } } { ( x + 2 ) ^ { 3 } } \cdot \frac { x ^ { 2 } + 4 x + 4 } { x ^ { 2 } + 6 x + 0 }$$

Evaluate

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

Short Solution Steps

Anything plus zero gives itself.

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

Multiply \frac{\left(x+3\right)^{3}}{\left(x+2\right)^{3}} times \frac{x^{2}+4x+4}{x^{2}+6x} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x+2\right)^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}+9x^{2}+27x+27}{x^{3}+8x^{2}+12x}$$

Expand

$$\frac{x^{3}+9x^{2}+27x+27}{\left(x+2\right)\left(x^{2}+6x\right)}$$

Short Solution Steps

Anything plus zero gives itself.

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

Multiply \frac{\left(x+3\right)^{3}}{\left(x+2\right)^{3}} times \frac{x^{2}+4x+4}{x^{2}+6x} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x+2\right)^{2} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}+9x^{2}+27x+27}{x^{3}+8x^{2}+12x}$$