Solve 1-4/x^2/frac{3{x}-6/x^2}

$$\frac { 1 - \frac { 4 } { x ^ { 2 } } } { \frac { 3 } { x } - \frac { 6 } { x ^ { 2 } } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Since \frac{3x}{x^{2}} and \frac{6}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}-4}{x^{2}} by \frac{3x-6}{x^{2}} by multiplying \frac{x^{2}-4}{x^{2}} by the reciprocal of \frac{3x-6}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Since \frac{3x}{x^{2}} and \frac{6}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}-4}{x^{2}} by \frac{3x-6}{x^{2}} by multiplying \frac{x^{2}-4}{x^{2}} by the reciprocal of \frac{3x-6}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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