Solve x^2-3x/(x+1)(x-4x^2)*2(x^2-3)/6+2x^2

$$\frac { x ^ { 2 } - 3 x } { ( x + 1 ) ( x - 4 x ^ { 2 } ) } \cdot \frac { 2 ( x ^ { 2 } - 3 ) } { 6 + 2 x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x}{\left(x+1\right)\left(x-4x^{2}\right)}.

$$\frac{x\left(x-3\right)}{x\left(x+1\right)\left(-4x+1\right)}\times \frac{2\left(x^{2}-3\right)}{6+2x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{x-3}{\left(x+1\right)\left(-4x+1\right)}\times \frac{2\left(x^{2}-3\right)}{6+2x^{2}}$$

Factor the expressions that are not already factored in \frac{2\left(x^{2}-3\right)}{6+2x^{2}}.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x-3}{\left(x+1\right)\left(-4x+1\right)} times \frac{x^{2}-3}{x^{2}+3} by multiplying numerator times numerator and denominator times denominator.

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

Use the distributive property to multiply x-3 by x^{2}-3.

$$\frac{x^{3}-3x-3x^{2}+9}{\left(x+1\right)\left(-4x+1\right)\left(x^{2}+3\right)}$$

Use the distributive property to multiply x+1 by -4x+1 and combine like terms.

$$\frac{x^{3}-3x-3x^{2}+9}{\left(-4x^{2}-3x+1\right)\left(x^{2}+3\right)}$$

Use the distributive property to multiply -4x^{2}-3x+1 by x^{2}+3 and combine like terms.

$$\frac{x^{3}-3x-3x^{2}+9}{-4x^{4}-11x^{2}-3x^{3}-9x+3}$$

Expand

$$\frac{x^{3}-3x^{2}-3x+9}{\left(1-4x\right)\left(x+1\right)\left(x^{2}+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x}{\left(x+1\right)\left(x-4x^{2}\right)}.

$$\frac{x\left(x-3\right)}{x\left(x+1\right)\left(-4x+1\right)}\times \frac{2\left(x^{2}-3\right)}{6+2x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{x-3}{\left(x+1\right)\left(-4x+1\right)}\times \frac{2\left(x^{2}-3\right)}{6+2x^{2}}$$

Factor the expressions that are not already factored in \frac{2\left(x^{2}-3\right)}{6+2x^{2}}.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x-3}{\left(x+1\right)\left(-4x+1\right)} times \frac{x^{2}-3}{x^{2}+3} by multiplying numerator times numerator and denominator times denominator.

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

Use the distributive property to multiply x-3 by x^{2}-3.

$$\frac{x^{3}-3x-3x^{2}+9}{\left(x+1\right)\left(-4x+1\right)\left(x^{2}+3\right)}$$

Use the distributive property to multiply x+1 by -4x+1 and combine like terms.

$$\frac{x^{3}-3x-3x^{2}+9}{\left(-4x^{2}-3x+1\right)\left(x^{2}+3\right)}$$

Use the distributive property to multiply -4x^{2}-3x+1 by x^{2}+3 and combine like terms.

$$\frac{x^{3}-3x-3x^{2}+9}{-4x^{4}-11x^{2}-3x^{3}-9x+3}$$