Solve 1/x+1/x^2+3/x^3/x^5-6x^2+1

$$\frac { \frac { 1 } { x } + \frac { 1 } { x ^ { 2 } } + \frac { 3 } { x ^ { 3 } } } { x ^ { 5 } - 6 x ^ { 2 } + 1 }$$

Evaluate

$$\frac{x^{2}+x+3}{x^{3}\left(x^{5}-6x^{2}+1\right)}$$

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{1}{x^{2}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{x+1}{x^{2}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{\left(x+1\right)x}{x^{3}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{\left(x+1\right)x+3}{x^{3}}}{x^{5}-6x^{2}+1}$$

Do the multiplications in \left(x+1\right)x+3.

$$\frac{\frac{x^{2}+x+3}{x^{3}}}{x^{5}-6x^{2}+1}$$

Express \frac{\frac{x^{2}+x+3}{x^{3}}}{x^{5}-6x^{2}+1} as a single fraction.

$$\frac{x^{2}+x+3}{x^{3}\left(x^{5}-6x^{2}+1\right)}$$

Use the distributive property to multiply x^{3} by x^{5}-6x^{2}+1.

$$\frac{x^{2}+x+3}{x^{8}-6x^{5}+x^{3}}$$

Expand

$$\frac{x^{2}+x+3}{x^{3}\left(x^{5}-6x^{2}+1\right)}$$

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{1}{x^{2}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{x+1}{x^{2}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{\left(x+1\right)x}{x^{3}}+\frac{3}{x^{3}}}{x^{5}-6x^{2}+1}$$

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

$$\frac{\frac{\left(x+1\right)x+3}{x^{3}}}{x^{5}-6x^{2}+1}$$

Do the multiplications in \left(x+1\right)x+3.

$$\frac{\frac{x^{2}+x+3}{x^{3}}}{x^{5}-6x^{2}+1}$$

Express \frac{\frac{x^{2}+x+3}{x^{3}}}{x^{5}-6x^{2}+1} as a single fraction.

$$\frac{x^{2}+x+3}{x^{3}\left(x^{5}-6x^{2}+1\right)}$$

Use the distributive property to multiply x^{3} by x^{5}-6x^{2}+1.

$$\frac{x^{2}+x+3}{x^{8}-6x^{5}+x^{3}}$$