e) \( \frac{3 \cdot 7^{x}-7^{x-1}}{2^{x}+2^{x}+2} \)

Calculate or simplify the expression \( (3*7^x-7^(x-1))/(2^x+2^x+2) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(3\times 7^{x}-7^{x-1}\right)}{\left(2^{x}+2^{x}+2\right)}\) - step1: Remove the parentheses: \(\frac{3\times 7^{x}-7^{x-1}}{2^{x}+2^{x}+2}\) - step2: Add the terms: \(\frac{3\times 7^{x}-7^{x-1}}{2^{x+1}+2}\) - step3: Rewrite the expression: \(\frac{\frac{20}{7}\times 7^{x}}{2\times 2^{x}+2}\) - step4: Rewrite the expression: \(\frac{\frac{20\times 7^{x}}{7}}{2\times 2^{x}+2}\) - step5: Multiply by the reciprocal: \(\frac{20\times 7^{x}}{7}\times \frac{1}{2\times 2^{x}+2}\) - step6: Rewrite the expression: \(\frac{20\times 7^{x}}{7}\times \frac{1}{2\left(2^{x}+1\right)}\) - step7: Reduce the fraction: \(\frac{10\times 7^{x}}{7}\times \frac{1}{2^{x}+1}\) - step8: Multiply the terms: \(\frac{10\times 7^{x}}{7\left(2^{x}+1\right)}\) - step9: Calculate: \(\frac{10\times 7^{x}}{7\times 2^{x}+7}\) - step10: Calculate: \(\frac{10\times 7^{x-1}\times 7}{\left(2^{x}+1\right)\times 7}\) - step11: Reduce the fraction: \(\frac{10\times 7^{x-1}}{2^{x}+1}\) The simplified form of the expression \( \frac{3 \cdot 7^{x}-7^{x-1}}{2^{x}+2^{x}+2} \) is \( \frac{10 \times 7^{x-1}}{2^{x}+1} \).