Solve 6x-3x/x^2-left(3xright)^2-x-3x/x+3x

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

Evaluate

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

Short Solution Steps

Combine 6x and -3x to get 3x.

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

Expand \left(3x\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

Combine x^{2} and -9x^{2} to get -8x^{2}.

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

Cancel out x in both numerator and denominator.

$$\frac{3}{-8x}-\frac{x-3x}{x+3x}$$

Combine x and -3x to get -2x.

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

Combine x and 3x to get 4x.

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

Cancel out 2x in both numerator and denominator.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -8x and 2 is 8x. Multiply \frac{3}{-8x} times \frac{-1}{-1}. Multiply \frac{1}{2} times \frac{4x}{4x}.

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

Since \frac{3\left(-1\right)}{8x} and \frac{4x}{8x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(-1\right)+4x.

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

Expand

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

Short Solution Steps

Combine 6x and -3x to get 3x.

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

Expand \left(3x\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

Combine x^{2} and -9x^{2} to get -8x^{2}.

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

Cancel out x in both numerator and denominator.

$$\frac{3}{-8x}-\frac{x-3x}{x+3x}$$

Combine x and -3x to get -2x.

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

Combine x and 3x to get 4x.

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

Cancel out 2x in both numerator and denominator.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -8x and 2 is 8x. Multiply \frac{3}{-8x} times \frac{-1}{-1}. Multiply \frac{1}{2} times \frac{4x}{4x}.

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

Since \frac{3\left(-1\right)}{8x} and \frac{4x}{8x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\left(-1\right)+4x.

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