1) [latex] \frac{1}{2p+4q} [/latex] - [latex] \frac{q}{4q x^{2}- p^{2}} [/latex]=??? 2) [latex] \frac{1}{ a^{2}+ab+ b^{2} } + \frac{b}{ a^{2}-b^{3}} [/latex]=??? 3)[latex] \frac{ m^{2}+ n^{2}}{ m^{3} + n^{3}}- \frac{1}{2(m+n)} ...

[latex]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} } [/latex] [latex]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} )}[/latex]