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

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

Evaluate

$$1+\frac{4}{x}+\frac{3}{x^{2}}+\frac{1}{x^{3}}$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+1+\left(x+3\right)x^{2}.

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

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

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

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

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

Do the multiplications in x+1+x^{3}+3x^{2}+\left(x+2\right)x.

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

Combine like terms in x+1+x^{3}+3x^{2}+x^{2}+2x.

$$\frac{3x+1+x^{3}+4x^{2}}{x^{3}}$$

Expand

$$1+\frac{4}{x}+\frac{3}{x^{2}}+\frac{1}{x^{3}}$$

Short Solution Steps

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

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

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

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

Do the multiplications in x+1+\left(x+3\right)x^{2}.

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

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

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

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

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

Do the multiplications in x+1+x^{3}+3x^{2}+\left(x+2\right)x.

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

Combine like terms in x+1+x^{3}+3x^{2}+x^{2}+2x.

$$\frac{3x+1+x^{3}+4x^{2}}{x^{3}}$$