Question

simplify: 16×2^n+1 - 4×2^n/16×2^n+2 -2×2^n+2

Answer 1

$\red{\underline{Hey\: mate\: !}}$

$\frac{(16\times 2^{n}\times2) - (4\times 2^{n})}{(16\times 2^{n+2})-(2\times 2^{n+2})}\\\\\implies \frac{(16\times 2^{n}\times 2)-(4\times2^{n})}{(16\times 2^{n}\times 2^{2})- 2\times 2^{n}\times 2^{2}}\\\\\implies \frac{\cancel{4\times 2^{n}}(4\times 2 -1)}{\cancel{4\times 2^{n}}(16-2)}\\\\\implies \frac{(8-1)}{(16-2)}\\\\\implies \frac{\cancel 7}{\cancel {14}}\\\\\implies \frac{1}{2}$

$\boxed{\pink{ Answer\implies \frac{1}{2}}}$

Answer 2

Hello!

$\dfrac{(16 \sf \:x\: 2^{n} \sf \:x\: 2) - (4 \sf \:x\: 2^{n})}{(16 \sf \:x\: 2^{n+2}) - 2 \sf \:x\: 2^{n+2})}$

⇒ $\dfrac{(16 \sf \:x\: 2^{n} \sf \:x\: 2) - (4 \sf \:x\: 2^{n})}{(16 \sf \:x\: 2^{n} \sf \:x\:2^{2}) - (2 \sf \:x\: 2^{n} \sf \:x\:2^{2})}$

⇒ $\dfrac{\cancel{4 \sf \:x\: 2^{n}}(4 \sf \:x\:2 - 1)}{\cancel{4 \sf \:x\: 2^{n}}(16-2)}$

⇒ $\dfrac{8-1}{16-2}$ ⇒ $\dfrac{7}{14} = \boxed{\blue{\bf{\dfrac{1}{2}}}}$

Cheers!