Solve x^4+1/x^2/x^2-3x+1

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{x^{2}}{x^{2}}.

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

Since \frac{x^{4}x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{4}x^{2}+1.

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

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

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

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

$$\frac{x^{6}+1}{x^{4}-3x^{3}+x^{2}}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{x^{2}}{x^{2}}.

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

Since \frac{x^{4}x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{4}x^{2}+1.

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

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

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

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

$$\frac{x^{6}+1}{x^{4}-3x^{3}+x^{2}}$$