Solve x^2-3x+1divx^5-4x^3+x^2+3x+1

$${ x }^{ 2 } -3x+1 \div { x }^{ 5 } -4 { x }^{ 3 } + { x }^{ 2 } +3x+1$$

Evaluate

$$-4x^{3}+2x^{2}+1+\frac{1}{x^{5}}$$

Short Solution Steps

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-3x+\frac{1}{x^{5}}-4x^{3}+3x+1$$

Combine -3x and 3x to get 0.

$$2x^{2}+\frac{1}{x^{5}}-4x^{3}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}-4x^{3}+1 times \frac{x^{5}}{x^{5}}.

$$\frac{\left(2x^{2}-4x^{3}+1\right)x^{5}}{x^{5}}+\frac{1}{x^{5}}$$

Since \frac{\left(2x^{2}-4x^{3}+1\right)x^{5}}{x^{5}} and \frac{1}{x^{5}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{2}-4x^{3}+1\right)x^{5}+1}{x^{5}}$$

Do the multiplications in \left(2x^{2}-4x^{3}+1\right)x^{5}+1.

$$\frac{2x^{7}-4x^{8}+x^{5}+1}{x^{5}}$$

Factor

$$-\frac{\left(x-1\right)\left(4x^{7}+2x^{6}+2x^{5}+x^{4}+x^{3}+x^{2}+x+1\right)}{x^{5}}$$