simpity \( \frac{2 x^{5}}{x^{5}}+\frac{2}{x^{5}} \)

Simplify the expression by following steps: - step0: Solution: \(\frac{2x^{5}}{x^{5}}+\frac{2}{x^{5}}\) - step1: Transform the expression: \(\frac{2x^{5}+2}{x^{5}}\) Calculate or simplify the expression \( 2x^{5}+2 \). Simplify the expression by following steps: - step0: Solution: \(2x^{5}+2\) Factor the expression \( 2x^{5}+2 \). Factor the expression by following steps: - step0: Factor: \(2x^{5}+2\) - step1: Factor the expression: \(2\left(x^{5}-x^{4}+x^{3}-x^{2}+x+x^{4}-x^{3}+x^{2}-x+1\right)\) - step2: Factor the expression: \(2\left(x\left(x^{4}-x^{3}+x^{2}-x+1\right)+x^{4}-x^{3}+x^{2}-x+1\right)\) - step3: Factor the expression: \(2\left(x+1\right)\left(x^{4}-x^{3}+x^{2}-x+1\right)\) Let's simplify the expression \( \frac{2 x^{5}}{x^{5}}+\frac{2}{x^{5}} \) step by step. 1. **Simplify the first term**: \[ \frac{2 x^{5}}{x^{5}} = 2 \] because \( x^{5} \) in the numerator and denominator cancels out. 2. **Combine the terms**: Now we have: \[ 2 + \frac{2}{x^{5}} \] 3. **Combine into a single fraction**: To combine these terms into a single fraction, we can express \( 2 \) as \( \frac{2x^{5}}{x^{5}} \): \[ \frac{2x^{5}}{x^{5}} + \frac{2}{x^{5}} = \frac{2x^{5} + 2}{x^{5}} \] 4. **Factor the numerator**: The numerator \( 2x^{5} + 2 \) can be factored: \[ 2(x^{5} + 1) \] Thus, we have: \[ \frac{2(x^{5} + 1)}{x^{5}} \] 5. **Final expression**: The simplified expression is: \[ \frac{2(x^{5} + 1)}{x^{5}} \] This is the final simplified form of the original expression.