Question

Factories (x+1/x)^2+6(x+1/x)+9

Answer 1

${ ( \frac{x + 1}{x} ) }^{2} + 6( \frac{x + 1}{x} ) + 9 \\ \\ = ( \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} } ) + ( \frac{6x + 6}{x} ) + 9 \\ \\ making \: all \: denominators \: same \\ \\ \frac{ {x}^{2} + 2x + 1 + 6 {x}^{2} + 6x + 9 {x}^{2} }{ {x}^{2} } \\ \\ = \frac{16 {x}^{2} + 8x + 1}{ {x}^{2} } \\ \\ = \frac{16 {x}^{2} + 4x + 4x + 1 }{ {x}^{2} } \\ \\ \frac{4x(4x + 1) + (4x + 1)}{ {x}^{2} } \\ \\ = \frac{ {(4x + 1)}^{2} }{ {x}^{2} }$


♡♡♡