Solve 2+6/x/2-frac{6{x^2}}

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{2x}{x} and \frac{6}{x} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

Since \frac{2x}{x} and \frac{6}{x} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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