Solve (2/x+1/x^2)dx

$$( \frac { 2 } { x } + \frac { 1 } { x ^ { 2 } } ) d x$$

Evaluate

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

Short Solution Steps

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{2}{x} times \frac{x}{x}.

$$\left(\frac{2x}{x^{2}}+\frac{1}{x^{2}}\right)dx$$

Since \frac{2x}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{2x+1}{x^{2}}dx$$

Express \frac{2x+1}{x^{2}}d as a single fraction.

$$\frac{\left(2x+1\right)d}{x^{2}}x$$

Express \frac{\left(2x+1\right)d}{x^{2}}x as a single fraction.

$$\frac{\left(2x+1\right)dx}{x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{d\left(2x+1\right)}{x}$$

Use the distributive property to multiply d by 2x+1.

$$\frac{2dx+d}{x}$$

Expand

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

Short Solution Steps

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{2}{x} times \frac{x}{x}.

$$\left(\frac{2x}{x^{2}}+\frac{1}{x^{2}}\right)dx$$

Since \frac{2x}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{2x+1}{x^{2}}dx$$

Express \frac{2x+1}{x^{2}}d as a single fraction.

$$\frac{\left(2x+1\right)d}{x^{2}}x$$

Express \frac{\left(2x+1\right)d}{x^{2}}x as a single fraction.

$$\frac{\left(2x+1\right)dx}{x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{d\left(2x+1\right)}{x}$$

Use the distributive property to multiply d by 2x+1.

$$\frac{2dx+d}{x}$$