Question

(2x+1)^2+(2x-1)^2/(2x+1)^2- (2x-1)^2​

Answer 1

$\: \: \: \sf \frac{ {(2x + 1)}^{2} + {(2x - 1)}^{2} }{ {(2x + 1)}^{2} - {(2x - 1)}^{2} } \\ \\ \tt \to \frac{ {4x}^{2} \cancel{ + 4x} + 1 + {4x}^{2} \cancel{- 4x} + 1 }{ {4x}^{2} + 4x + 1 - ( {4x}^{2} - 4x + 1)} \\ \\ \tt \to \frac{ {(4 + 4)x}^{2} + 2 }{\cancel{ {4x}^{2} } + 4x \cancel{+ 1} \cancel{- {4x}^{2}} + 4x \cancel{- 1 }} \\ \\ \tt \to \frac{ {8x}^{2} + 2}{8x} \: \: \to \frac{\cancel2( {4x}^{2} + 1 )}{ \cancel2(4x)} \\ \\ \tt \to \: \: \frac{ {4x}^{2} + 1 }{4x} \: \: \to \frac{ {\cancel4x}^{ \cancel2} }{\cancel4\cancel{x}} + \frac{1}{4x} \\ \\ \tt \to \: \: \red{x + \frac{1}{4x} }$