Объяснение:

1)

[tex] \frac{a + b}{2a + 2 \sqrt{ab} } + \frac{ \sqrt{b} }{ \sqrt{a} + \sqrt{b} } = \frac{a + b}{2a + 2\sqrt{ab} } + \frac{2 \sqrt{b} \times \sqrt{a} }{ 2\sqrt{a} ( \sqrt{a} + \sqrt{b} ) } = \frac{a + b}{2a + 2 \sqrt{ab} } + \frac{2 \sqrt{ab} }{2 \sqrt{a} \times \sqrt{a} + 2 \sqrt{ab} } = \frac{a + b}{2a + 2 \sqrt{ab} } + \frac{2 \sqrt{ab} }{2a + 2 \sqrt{ab} } = \frac{a + 2 \sqrt{ab} + b }{2a + 2 \sqrt{ab} } = \frac{{( \sqrt{a} + \sqrt{b} ) }^{2} }{2 \sqrt{a} ( \sqrt{a} + \sqrt{b} )} = \frac{ \sqrt{a} + \sqrt{b} }{2 \sqrt{a} } [/tex]

2)

[tex] (\frac{ \sqrt{b} + 7 }{ \sqrt{b} - 7} - \frac{28 \sqrt{b} }{b - 49} ) \div \frac{ \sqrt{b} - 7 }{b + 7 \sqrt{b} } = ( \frac{ (\sqrt{b} + 7)( \sqrt{b} + 7) }{( \sqrt{b} - 7)( \sqrt{b} + 7) } - \frac{28 \sqrt{b} }{( \sqrt{b} - 7)( \sqrt{b} + 7)}) \times \frac{ \sqrt{b} ( \sqrt{b} + 7)}{ \sqrt{b} - 7 } = \frac{ {( \sqrt{b } + 7) }^{2} - 28 \sqrt{b} }{ (\sqrt{b} - 7)( \sqrt{b} + 7)} \times \frac{ \sqrt{b} ( \sqrt{b } + 7) }{ \sqrt{b} - 7} = \frac{ {( \sqrt{b} )}^{2} + 2 \times 7 \sqrt{b} + {7}^{2} - 28 \sqrt{b} }{ \sqrt{b} - 7 } \times \frac{ \sqrt{b} }{ \sqrt{b} - 7 } = \frac{(b + 49 + 14 \sqrt{b} - 28 \sqrt{b} ) \times \sqrt{b} }{ {( \sqrt{b} - 7)}^{2} } = \frac{(b - 14 \sqrt{b} + 49) \sqrt{b} }{ {( \sqrt{b} )}^{2} - 2 \times 7\sqrt{b} + {7}^{2} } = \frac{(b - 14 \sqrt{b} + 49) \sqrt{b} }{b - 14 \sqrt{b} + 49 } = \sqrt{b} [/tex]