Solve sqrt{13}(x+x^4)(1-1/x)^5

$$\sqrt { 13 } ( x + x ^ { 4 } ) ( 1 - \frac { 1 } { x } ) ^ { 5 }$$

Evaluate

$$\frac{\sqrt{13}\left(x^{3}+1\right)\left(x-1\right)^{5}}{x^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\sqrt{13}\left(x+x^{4}\right)\left(\frac{x}{x}-\frac{1}{x}\right)^{5}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{13}\left(x+x^{4}\right)\times \left(\frac{x-1}{x}\right)^{5}$$

To raise \frac{x-1}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{13}\left(x+x^{4}\right)\times \frac{\left(x-1\right)^{5}}{x^{5}}$$

Express \sqrt{13}\times \frac{\left(x-1\right)^{5}}{x^{5}} as a single fraction.

$$\frac{\sqrt{13}\left(x-1\right)^{5}}{x^{5}}\left(x+x^{4}\right)$$

Express \frac{\sqrt{13}\left(x-1\right)^{5}}{x^{5}}\left(x+x^{4}\right) as a single fraction.

$$\frac{\sqrt{13}\left(x-1\right)^{5}\left(x+x^{4}\right)}{x^{5}}$$

Factor the expressions that are not already factored.

$$\frac{\sqrt{13}x\left(x+1\right)\left(x^{2}-x+1\right)\left(x-1\right)^{5}}{x^{5}}$$

Cancel out x in both numerator and denominator.

$$\frac{\sqrt{13}\left(x+1\right)\left(x^{2}-x+1\right)\left(x-1\right)^{5}}{x^{4}}$$

Expand the expression.

$$\frac{\sqrt{13}x^{8}-5\sqrt{13}x^{7}+10\sqrt{13}x^{6}-9\sqrt{13}x^{5}+9\sqrt{13}x^{3}-10\sqrt{13}x^{2}+5\sqrt{13}x-\sqrt{13}}{x^{4}}$$

Factor

$$\frac{\sqrt{13}\left(x+1\right)\left(x^{2}-x+1\right)\left(x-1\right)^{5}}{x^{4}}$$