Solve x^2+5x+6/4x^2+12x*x^3/x^2-4

$$\frac{ { x }^{ 2 } +5x+6 }{ 4 { x }^{ 2 } +12x } \times \frac{ { x }^{ 3 } }{ { x }^{ 2 } -4 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+5x+6}{4x^{2}+12x}.

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

Cancel out x+3 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}}{4x-8}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+5x+6}{4x^{2}+12x}.

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

Cancel out x+3 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}}{4x-8}$$