Solve frac{x^{3}+x^2-4x-4}{x^2-2x-15}*x^2+8x+15/3x^2-8

$$\frac { x ^ { 3 } + x ^ { 2 } - 4 x - 4 } { x ^ { 2 } - 2 x - 15 } \cdot \frac { x ^ { 2 } + 8 x + 15 } { 3 x ^ { 2 } - 8 }$$

Evaluate

$$\frac{\left(x+1\right)\left(x+5\right)\left(x^{2}-4\right)}{\left(x-5\right)\left(3x^{2}-8\right)}$$

Short Solution Steps

Multiply \frac{x^{3}+x^{2}-4x-4}{x^{2}-2x-15} times \frac{x^{2}+8x+15}{3x^{2}-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{3}+x^{2}-4x-4\right)\left(x^{2}+8x+15\right)}{\left(x^{2}-2x-15\right)\left(3x^{2}-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-2\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(3x^{2}-8\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{\left(x-2\right)\left(x+1\right)\left(x+2\right)\left(x+5\right)}{\left(x-5\right)\left(3x^{2}-8\right)}$$

Expand the expression.

$$\frac{x^{4}+6x^{3}+x^{2}-24x-20}{3x^{3}-15x^{2}-8x+40}$$

Expand

$$\frac{x^{4}+6x^{3}+x^{2}-24x-20}{\left(x-5\right)\left(3x^{2}-8\right)}$$

Short Solution Steps

Multiply \frac{x^{3}+x^{2}-4x-4}{x^{2}-2x-15} times \frac{x^{2}+8x+15}{3x^{2}-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{3}+x^{2}-4x-4\right)\left(x^{2}+8x+15\right)}{\left(x^{2}-2x-15\right)\left(3x^{2}-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-2\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(3x^{2}-8\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{\left(x-2\right)\left(x+1\right)\left(x+2\right)\left(x+5\right)}{\left(x-5\right)\left(3x^{2}-8\right)}$$

Expand the expression.

$$\frac{x^{4}+6x^{3}+x^{2}-24x-20}{3x^{3}-15x^{2}-8x+40}$$