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

Question

UpStudy AI · Accepted Answer

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

e)

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