Solve x+3/x^3+8-3x-1/x^3+8-2-2x/x^3+8

$$\frac{ x+3 }{ { x }^{ 3 } +8 } - \frac{ 3x-1 }{ { x }^{ 3 } +8 } - \frac{ 2-2x }{ { x }^{ 3 } +8 }$$

Evaluate

$$\frac{2}{x^{3}+8}$$

Short Solution Steps

Since \frac{x+3}{x^{3}+8} and \frac{3x-1}{x^{3}+8} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+3-\left(3x-1\right).

$$\frac{x+3-3x+1}{x^{3}+8}-\frac{2-2x}{x^{3}+8}$$

Combine like terms in x+3-3x+1.

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

Since \frac{-2x+4}{x^{3}+8} and \frac{2-2x}{x^{3}+8} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -2x+4-\left(2-2x\right).

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

Combine like terms in -2x+4-2+2x.

$$\frac{2}{x^{3}+8}$$

Expand

$$\frac{2}{x^{3}+8}$$

Short Solution Steps

Since \frac{x+3}{x^{3}+8} and \frac{3x-1}{x^{3}+8} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+3-\left(3x-1\right).

$$\frac{x+3-3x+1}{x^{3}+8}-\frac{2-2x}{x^{3}+8}$$

Combine like terms in x+3-3x+1.

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

Since \frac{-2x+4}{x^{3}+8} and \frac{2-2x}{x^{3}+8} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -2x+4-\left(2-2x\right).

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

Combine like terms in -2x+4-2+2x.

$$\frac{2}{x^{3}+8}$$