\( \frac{9^{x}-9}{3^{x}-3} \) Exponents and surds

Calculate or simplify the expression \( (9^x-9)/(3^x-3) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(9^{x}-9\right)}{\left(3^{x}-3\right)}\) - step1: Remove the parentheses: \(\frac{9^{x}-9}{3^{x}-3}\) - step2: Evaluate: \(\frac{3\left(3^{2x-1}-3\right)}{3\left(3^{x-1}-1\right)}\) - step3: Evaluate: \(\frac{3^{2x-1}-3}{3^{x-1}-1}\) - step4: Rewrite the expression: \(\frac{\frac{1}{3}\left(3^{x}\right)^{2}-3}{\frac{1}{3}\times 3^{x}-1}\) - step5: Rewrite the expression: \(\frac{\frac{\left(3^{x}\right)^{2}-9}{3}}{\frac{1}{3}\times 3^{x}-1}\) - step6: Rewrite the expression: \(\frac{\frac{\left(3^{x}\right)^{2}-9}{3}}{\frac{3^{x}-3}{3}}\) - step7: Multiply by the reciprocal: \(\frac{\left(3^{x}\right)^{2}-9}{3}\times \frac{3}{3^{x}-3}\) - step8: Rewrite the expression: \(\frac{\left(3^{x}-3\right)\left(3^{x}+3\right)}{3}\times \frac{3}{3^{x}-3}\) - step9: Reduce the fraction: \(\left(3^{x}+3\right)\times 1\) - step10: Multiply the terms: \(3^{x}+3\) The simplified form of the expression \( \frac{9^{x}-9}{3^{x}-3} \) is \( 3^{x}+3 \).