б) (m²+n²)/(m³+n³) -1/2(m+n) = (2(m²+n²) -(m²-mn +n²))/2(m+n)(m²-mn+n²) =
(2m²+2n² -m²+mn -n²))/2(m+n)(m²-mn+n²) = (m²+mn+n² )/2(m+n)(m²-mn+n²) =
(m²+mn+n² )/2(m³+n³).
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г) 2(p+q)/(p³ -q³)+2/(q² -p²) = 2(p+q)/(p³ -q³)-2/(p² -q²) = 2(p+q)/(p -q)(p²+pq+q²)-2/(p -q)(p +q) =
(2(p+q)² -2(p²+pq+q²) )/(p-q)(p²+pq+q²)(p+q) =
2( (p²+2pq+q²) - (p²+pq+q²)) /(p-q)(p²+pq+q²)(p+q)=
2(p²+2pq+q² - p² -pq-q²)/(p-q)(p²+pq+q²)(p+q)=2pq/(p-q)(p²+pq+q²)(p+q) . или
2pq/(p³-q³)(p+q) .
* * * * * * *
применялись формулы сокращенного умножения :
m³+n³ =(m+n)(m² - mn+n²) ;
m³-n³ =(m-n)(m² + mn+n²) ;
m² - n²= (m - n)(m + n) ;
(m+n)²= m² +2mn+n² . .