Solve (3x^{3}-6x-2x^{2}*x^2):(4x^2*3x^2-8x*x^3)=

$$( 3 x ^ { 3 } - 6 x - 2 x ^ { 2 } \cdot x ^ { 2 } ) : ( 4 x ^ { 2 } \cdot 3 x ^ { 2 } - 8 x \cdot x ^ { 3 } ) =$$

Evaluate

$$-\frac{1}{2}+\frac{3}{4x}-\frac{3}{2x^{3}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{2}\times 3x^{2}-8xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{4}\times 3-8xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{4}\times 3-8x^{4}}$$

Multiply 4 and 3 to get 12.

$$\frac{3x^{3}-6x-2x^{4}}{12x^{4}-8x^{4}}$$

Combine 12x^{4} and -8x^{4} to get 4x^{4}.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand

$$-\frac{1}{2}+\frac{3}{4x}-\frac{3}{2x^{3}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{2}\times 3x^{2}-8xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{4}\times 3-8xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3x^{3}-6x-2x^{4}}{4x^{4}\times 3-8x^{4}}$$

Multiply 4 and 3 to get 12.

$$\frac{3x^{3}-6x-2x^{4}}{12x^{4}-8x^{4}}$$

Combine 12x^{4} and -8x^{4} to get 4x^{4}.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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