c) $$ \frac{9^{x}-9}{3^{x}-3} $$

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UpStudy AI · Accepted Answer

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

c)

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