Question

plz solve this question its urgent

Answer 1

( iii ) :

$\dfrac{x^{3} - 1}{x^{4}+x^{2}+1}$

$\dfrac{(x-1)(x^{2}+x+1)}{x^{4} -x^{3} + x^{2} +x^{3} - x^{2}+x+x^{2}-x+ 1}$

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

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

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

Answer : $\dfrac{x-1}{x^{2} - x+ 1 }$

( iv ) :

$\dfrac{x^{8}-y^{8}}{(x-y)(x^{4}+y^{4})}$

$\dfrac{(x^{4}-y^{4})(x^{4}+y^{4})}{(x-y)(x^{4}+y^{4})}$

$\dfrac{(x^{2}-y^{2})(x^{2}+y^{2})}{x-y}$

$\dfrac{(x-y)(x+y)(x^{2}+y^{2})}{x-y}$

( x + y )( x^2 + y^2 )

Answer :  ( x + y )( x^2 + y^2 )