Question

$(x-\frac{1}{x})^{2} - (x+\frac{1}{x})^{2}$

Answer 1

Answer:

$\tt \red{ \implies\left(\dfrac{xx}{x}-\dfrac{1}{x}\right)^{2}-\left( \dfrac{xx}{x} +\dfrac{1}{x}\right)^{2} }$

$\tt \pink{ \implies\left(\dfrac{x^{2}-1}{x}\right)^{2}-\left(\dfrac{ {x}^{2} + 1 }{x}\right)^{2} }$

$\tt \blue{ \implies\dfrac{\left(x^{2}-1\right)^{2}}{x^{2}} - \dfrac{\left(x^{2} + 1\right)^{2}}{x^{2}}}$

$\tt \orange{ \implies\dfrac{\left(x^{2}-1\right)^{2}-\left(x^{2}+1\right)^{2}}{x^{2}} }$

$\tt \green{ \implies\dfrac{x^{4}-2x^{2}+1-x^{4}-2x^{2}-1}{x^{2}} }$

$\boxed{ \tt \purple{ \implies\dfrac{-4 \cancel{x^{2}}} {\cancel{x^{2}}}}\boxed{\boxed{ = - 4 }}}$