Question

даю 85 балов!!!
смотри фото:

Answer 1

$\displaystyle\bf\\1) \ \ \frac{16x^{3} }{21y^{4} } :\frac{8x^{8} }{3y^{6} } =\frac{16x^{3} }{21y^{4} } \cdot\frac{3y^{6} }{8x^{8} } =\frac{2y^{2} }{7x^{5} } \\\\\\2) \ \ \frac{m^{2} +5m}{16m^{2} -1}:\frac{m^{4}+125m}{16m^{2} -8m+1} =\frac{m^{2} +5m}{16m^{2} -1}\cdot\frac{16m^{2} -8m+1}{m^{4} +125m} =\\\\\\=\frac{m(m+5)}{(4m-1)(4m+1)} \cdot\frac{(4m-1)^{2} }{m(m^{3} +125)} =\\\\\\=\frac{m+5}{4m+1} \cdot\frac{4m-1}{(m+5)(m^{2}-5m+25) } =\frac{4m-1}{(4m+1)(m^{2} -5m+25)}$

$\displaystyle\bf\\3) \ \ (\sqrt{2} +3)^{2} -3\sqrt{8} =(\sqrt{2} )^{2} +2\cdot\sqrt{2} \cdot3+3^{2} -3\sqrt{4\cdot2} =\\\\=2+6\sqrt{2} +9-3\cdot2\sqrt{2}=11+6\sqrt{2} -6\sqrt{2} =11$