Solve 2/x+3x+1/x^2+x-2/x^3

$$\frac{ 2 }{ x } + \frac{ 3x+1 }{ { x }^{ 2 } } + \frac{ x-2 }{ { x }^{ 3 } }$$

Evaluate

$$\frac{5x^{2}+2x-2}{x^{3}}$$

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}.

$$\frac{2x}{x^{2}}+\frac{3x+1}{x^{2}}+\frac{x-2}{x^{3}}$$

Since \frac{2x}{x^{2}} and \frac{3x+1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{2x+3x+1}{x^{2}}+\frac{x-2}{x^{3}}$$

Combine like terms in 2x+3x+1.

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

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{5x+1}{x^{2}} times \frac{x}{x}.

$$\frac{\left(5x+1\right)x}{x^{3}}+\frac{x-2}{x^{3}}$$

Since \frac{\left(5x+1\right)x}{x^{3}} and \frac{x-2}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5x+1\right)x+x-2}{x^{3}}$$

Do the multiplications in \left(5x+1\right)x+x-2.

$$\frac{5x^{2}+x+x-2}{x^{3}}$$

Combine like terms in 5x^{2}+x+x-2.

$$\frac{5x^{2}+2x-2}{x^{3}}$$

Expand

$$\frac{5x^{2}+2x-2}{x^{3}}$$

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}.

$$\frac{2x}{x^{2}}+\frac{3x+1}{x^{2}}+\frac{x-2}{x^{3}}$$

Since \frac{2x}{x^{2}} and \frac{3x+1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{2x+3x+1}{x^{2}}+\frac{x-2}{x^{3}}$$

Combine like terms in 2x+3x+1.

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

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{5x+1}{x^{2}} times \frac{x}{x}.

$$\frac{\left(5x+1\right)x}{x^{3}}+\frac{x-2}{x^{3}}$$

Since \frac{\left(5x+1\right)x}{x^{3}} and \frac{x-2}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5x+1\right)x+x-2}{x^{3}}$$

Do the multiplications in \left(5x+1\right)x+x-2.

$$\frac{5x^{2}+x+x-2}{x^{3}}$$

Combine like terms in 5x^{2}+x+x-2.

$$\frac{5x^{2}+2x-2}{x^{3}}$$