Question

Упростите выражения:

Answer 1

$a) frac{ m^{2} + n^{2} }{ m^{3} + n^{3} } - frac{1}{2(m+n)} = 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{m^{2}+mn+n^{2}}{2(m+n)(m^{2}-mn+n^{2})}$
$b) frac{2(p+q)}{p^{3}-q^{3}} + frac{2}{q^{2}-p^{2}} = frac{(p+q)(2p+2q)-(p^{2}+pq+q^{2})2}{(p-q)(p^{2}+pq+q^{2})(p+q)} = frac{2p^{2}+4pq+2q^{2}-2p^{2}-2pq-2q^{2}}{<span>(p-q)(p^{2}+pq+q^{2})(p+q)</span>}$ $= frac{2pq}{(p-q)(p^{2}+pq+q^{2})(p+q)}$