Solve 5+6/x/1-frac{4{x^2}}

$$\frac { 5 + \frac { 6 } { x } } { 1 - \frac { 4 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x\left(5x+6\right)}{x^{2}-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x}{x}.

$$\frac{\frac{5x}{x}+\frac{6}{x}}{1-\frac{4}{x^{2}}}$$

Since \frac{5x}{x} and \frac{6}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5x+6}{x}}{1-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+6}{x}}{\frac{x^{2}}{x^{2}}-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+6}{x}}{\frac{x^{2}-4}{x^{2}}}$$

Divide \frac{5x+6}{x} by \frac{x^{2}-4}{x^{2}} by multiplying \frac{5x+6}{x} by the reciprocal of \frac{x^{2}-4}{x^{2}}.

$$\frac{\left(5x+6\right)x^{2}}{x\left(x^{2}-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(5x+6\right)}{x^{2}-4}$$

Use the distributive property to multiply x by 5x+6.

$$\frac{5x^{2}+6x}{x^{2}-4}$$

Expand

$$\frac{5x^{2}+6x}{x^{2}-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x}{x}.

$$\frac{\frac{5x}{x}+\frac{6}{x}}{1-\frac{4}{x^{2}}}$$

Since \frac{5x}{x} and \frac{6}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5x+6}{x}}{1-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+6}{x}}{\frac{x^{2}}{x^{2}}-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+6}{x}}{\frac{x^{2}-4}{x^{2}}}$$

Divide \frac{5x+6}{x} by \frac{x^{2}-4}{x^{2}} by multiplying \frac{5x+6}{x} by the reciprocal of \frac{x^{2}-4}{x^{2}}.

$$\frac{\left(5x+6\right)x^{2}}{x\left(x^{2}-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(5x+6\right)}{x^{2}-4}$$

Use the distributive property to multiply x by 5x+6.

$$\frac{5x^{2}+6x}{x^{2}-4}$$