Solve 5/x^2-10/x^3/frac{1{x^2}-4/x^4}

$$\frac { \frac { 5 } { x ^ { 2 } } - \frac { 10 } { x ^ { 3 } } } { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { x ^ { 4 } } }$$

Evaluate

$$\frac{5x}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x^{3} is x^{3}. Multiply \frac{5}{x^{2}} times \frac{x}{x}.

$$\frac{\frac{5x}{x^{3}}-\frac{10}{x^{3}}}{\frac{1}{x^{2}}-\frac{4}{x^{4}}}$$

Since \frac{5x}{x^{3}} and \frac{10}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-10}{x^{3}}}{\frac{1}{x^{2}}-\frac{4}{x^{4}}}$$

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

$$\frac{\frac{5x-10}{x^{3}}}{\frac{x^{2}}{x^{4}}-\frac{4}{x^{4}}}$$

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

$$\frac{\frac{5x-10}{x^{3}}}{\frac{x^{2}-4}{x^{4}}}$$

Divide \frac{5x-10}{x^{3}} by \frac{x^{2}-4}{x^{4}} by multiplying \frac{5x-10}{x^{3}} by the reciprocal of \frac{x^{2}-4}{x^{4}}.

$$\frac{\left(5x-10\right)x^{4}}{x^{3}\left(x^{2}-4\right)}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{x\left(5x-10\right)}{x^{2}-4}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{5x}{x+2}$$

Expand

$$\frac{5x}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x^{3} is x^{3}. Multiply \frac{5}{x^{2}} times \frac{x}{x}.

$$\frac{\frac{5x}{x^{3}}-\frac{10}{x^{3}}}{\frac{1}{x^{2}}-\frac{4}{x^{4}}}$$

Since \frac{5x}{x^{3}} and \frac{10}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-10}{x^{3}}}{\frac{1}{x^{2}}-\frac{4}{x^{4}}}$$

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

$$\frac{\frac{5x-10}{x^{3}}}{\frac{x^{2}}{x^{4}}-\frac{4}{x^{4}}}$$

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

$$\frac{\frac{5x-10}{x^{3}}}{\frac{x^{2}-4}{x^{4}}}$$

Divide \frac{5x-10}{x^{3}} by \frac{x^{2}-4}{x^{4}} by multiplying \frac{5x-10}{x^{3}} by the reciprocal of \frac{x^{2}-4}{x^{4}}.

$$\frac{\left(5x-10\right)x^{4}}{x^{3}\left(x^{2}-4\right)}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{x\left(5x-10\right)}{x^{2}-4}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{5x}{x+2}$$