Question

please solve this question urgent..

Answer 1

1/(( x^(p-q). +1)

1/( x^p/x^q +1)

1/( x^p + x^q)/x^q

x^q)/ ( x^p + x^q)

x^p /( x^p + x^q). + x^q)/( x^p +x^q)

x^p + x^q)/ ( x^p + x^q)

1

Answer 2

$\frac{ {x}^{p} }{ {x}^{p} + {x}^{q} } + \frac{1}{ {x}^{p - q} + 1}$

LCM of X^p+X^q and x^p-q+1

=(x^p+x^q)(x^p-q+1)

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

As we know x^p×x^p=x^p+p=x^2p

$\frac{ {x}^{p}( {x}^{p - q} + 1) + 1( {x}^{p} + {x}^{q} ) }{( {x}^{p} + {x}^{q} )( {x}^{p - q} + 1) } \\ \\ \cancel{\frac{ {x}^{2p - q} + {x}^{p} + {x}^{p} + {x}^{q} }{ {x}^{2p - q} + {x}^{p} + {x}^{p} + {x}^{q} }} \\ \\ = 1$

Now

Some Steps You might not Understand

${x}^{p} (x {}^{p - q} ) \\ \\ { x }^{p + p - q} \\ \\ {x}^{2p - q}$

Another

${x}^{q} ( {x}^{p - q} ) \\ \\ {x}^{p - q + q} \\ \\ {x}^{p}$

$\huge{Answer = 1}$