Question

simplify-2^n+2^n-1/2^n+1- 2^n​

Answer 1

Answer:

$\dfrac{2^n+2^n-1}{2^n+1-2^n}=2^{1+n}-1$

Step-by-step explanation:

$\dfrac{2^n+2^n-1}{2^n+1-2^n}$

$2^n+2^n-1$

$\mathrm{Add\:similar\:elements:}\:2^n+2^n=2\cdot \:2^n$

$=2\cdot \:2^n-1$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$2\cdot \:2^n=\:2^{1+n}$

$=2^{n+1}-1$

$=\dfrac{2^{n+1}-1}{2^n+1-2^n}$

$\mathrm{Add\:similar\:elements:}\:2^n-2^n=0$

$=\dfrac{2^{n+1}-1}{1}$

$\mathrm{Apply\:rule}\:\dfrac{a}{1}=a$

$=2^{n+1}-1$