Question

1) $frac{1}{2p+4q}$ - $frac{q}{4q x^{2}- p^{2}}$=???
2) $frac{1}{ a^{2}+ab+ b^{2} } + frac{b}{ a^{2}-b^{3}}$=???
3)$frac{ m^{2}+ n^{2}}{ m^{3} + n^{3}}- frac{1}{2(m+n)}$=???

Answer 1

$1) .....= frac{1}{2(p+2q)}- frac{q}{(2q-p)(2q+p)}= frac{2q-p-2q}{2(2q-p)(2q+p)}= frac{-p}{8q^{2}-2p^{2} } \ \ 2) ...........= frac{1}{a^{2}+ab+b^{2} }+ frac{b}{(a-b)(a^{2}+ab+b^{2}) }= frac{a-b+b}{a^{3} - b^{3} } = frac{a}{a^{3}- b^{3} }$

$3) ......= frac{ m^{2} + n^{2} }{(m+n)(m^{2}-mn+ n^{2})}- frac{1}{2(m+n)}= frac{2(m^{2} +n^{2})- m^{2}+mn-n^{2} }{2(m+n)(m^{2}-mn+ n^{2})}= \ frac{2m^{2}+ 2n^{2}-m^{2}+mn-n^{2} }{2(m+n)( m^{2}-mn+n^{2}) } } = frac{m^{2}+mn+n^{2} }{2( m^{3} +n^{3} )}$